All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
ACT Exam  >  ACT Questions  >  The first and second terms of a geometr... Start Learning for Free
The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?
  • a)
    (ab)642
  • b)
    (ab)643
  • c)
    a642b
  • d)
    a643b
  • e)
    ab642
Correct answer is option 'E'. Can you explain this answer?
Clear all your ACT doubts with EduRev
Verified Answer
The first and second terms of a geometric sequence are a and ab,...
Refer to the following chart to follow the patter of the sequence.

Since the power of b is one less than the number of term, the nth term will be abn−1. The 643rd term will then be ab643−1 = ab642.
View all questions of this test
Most Upvoted Answer
The first and second terms of a geometric sequence are a and ab,...
Given information:
- First term of geometric sequence: a
- Second term of geometric sequence: ab

Formula for the nth term of a geometric sequence:
The nth term of a geometric sequence is given by: \(a_n = a \cdot r^{(n-1)}\), where
- a is the first term of the sequence
- r is the common ratio of the sequence

Finding the common ratio (r):
The second term of the sequence is a * r, so we have:
\(ab = a \cdot r\)
\(r = b\)

Calculating the 643rd term:
The 643rd term of the sequence can be written as:
\(a_{643} = a \cdot (b)^{642} = ab^{642}\)
Therefore, the 643rd term of the geometric sequence is \(ab^{642}\), which is option E.
Free Test
FREE
Start Free Test
Start Free Test
Community Answer
The first and second terms of a geometric sequence are a and ab,...
Refer to the following chart to follow the patter of the sequence.

Since the power of b is one less than the number of term, the nth term will be abn−1. The 643rd term will then be ab643−1 = ab642.
Explore Courses for ACT exam

Similar ACT Doubts

Directions:Read the passage and choose the best answer to each question.PassageWater pressure influences the rate at which water flows. As water pressure increases, so does the rate of flow. Water pressure can be defined as the amount of force that the water exerts on the container it is in. The more water that is in the container, the greater the water pressure will be. Some students conducted the following experiment:ExperimentStudents used tacks to punch holes in an empty plastic 2-liter bottle. The students created 4 holes, each 1-inch apart, from top to bottom. The tacks were left in each hole as the hole was created. The bottle was filled to the top with water and placed on a table. An 8 × 9-inch pan with a piece of blotting paper was placed lengthwise in front of the bottle. A ruler was placed in the pan to measure the spot at which the water stream touched the paper (range of water stream). The students removed the tack nearest the top of the bottle and marked the spot where the water stream touched the paper (range of water stream). The tack was then replaced, the bottle was filled to the top, and the next tack was removed.The spot where the water stream touched the paper was measured. Rate of flow was indicated by the length of the water stream. This procedure was repeated a total of 4 times, once for each tack. The results are recorded in Table 1 below.Q.Suppose that the students removed the tacks in order, replaced each tack after measuring the water stream, but did not re-fill the bottle after removing and replacing each tack. According to the passage, the water stream would most likely

Directions:Read the passages and choose the best answer to each question.PassageThe Earth’s magnetic field is one of its most significant natural phenomena. For centuries, the field has been used to aid navigation and exploration, and has been vital to many major discoveries. The magnetic field of the Earth extends several thousands of miles into space. It has the effect of shielding the Earth from solar wind, protecting the planet from dangerous high-energy particles and radiation. The exact source of the Earth’s magnetic field is not certain. The following two Scientists attempt to explain the phenomenon.Scientist 1The Earth’s magnetic field is similar to that of a bar magnet tilted 11 degrees from the spin axis of the Earth.The magnetic field of a bar magnet, or any other type of permanent magnet, is created by the coordinated motions of electrons within iron atoms. It is widely accepted that the Earth’s core consists of metals. The inner core is 70% as wide as the moon and consists of a solid iron ball, which would exhibit properties of ferromagnetism (the natural magnetic tendency of iron). The core has its own rotation and is surrounded by a “sea” of molten rock. The magnetic field grows and wanes, and the Earth’s poles drift and occasionally flip as the rotation of the core changes. The poles of the magnetic field have “flipped” many times due to the fluctuations in the rotation of the solid inner core. Other fluctuations in the magnetic field that can occur on a daily basis are largely the result of interference by solar wind.Scientist 2The Earth’s magnetic field is attributed to a dynamo effect of circulating electric current in the molten outer core. Electric currents cause magnetic fields; therefore, the circulating electric currents in the Earth’s molten metallic core are the origin of the magnetic field. When conducting fluid flows across an existing magnetic field, electric currents are induced, creating another magnetic field. When this magnetic field reinforces the original magnetic field, a dynamo is created which sustains itself.Sitting atop the hot, iron inner core, the Earth’s molten outer core churns and moves. The outer core also has cyclones or whirlpools powered by the Coriolis effects of Earth’s rotation. These complex and unpredictable motions generate the fluctuating magnetic field. The outer core is seething, swirling, and turbulent, which has been detected by the constant changes and reversals in polarity throughout the planet’s history. Further, iron has a special characteristic.When it is hotter than 1043 K, its Curie temperature, iron loses its magnetic properties. Therefore the Earth’s magnetic field is caused not by magnetised iron deposits, but mostly by electric currents in the liquid outer core.Q.A scientific article stated, “Since 1848, when the strength of the Earth’s magnetic field was first measured, the field has lost 10% of its strength.” Which of the scientists’ viewpoints, if any, is (ar e) in agreement with this statement?

Directions:Read the passages and choose the best answer to each question.PassageSea anemones look like plants, but they actually are predatory animals. They are invertebrates, which means that they do not have a skeleton. To protect themselves, they will attach to firm objects on the sea floor, such as rock or coral.Sea anemones can alter their body shape according to changes in their environment. For example, when ocean currents are strong, the sea anemone will reduce its internal volume in order to decrease the surface area that is exposed to the current. Sea anemones are dependent on water flow for food and nutrients and also for assistance in eliminating waste.Most anemones share a symbiotic relationship with marine algae called zooxanthellae. These are photosynthetic organisms whose waste products are a food source for the sea anemone. The sea anemone also enjoys a mutualistic relationship with the clown fish. This fish is immune to the stinging tentacles of the sea anemone, and it helps the anemone by actually cleaning the tentacles. The cleaning process yields food for the clown fish, while it remains protected from potential predators by the sea anemones stinging tentacles.Figure 1 shows a cross-section of portions of the internal anatomy of a sea anemone.Q.According to information in the passage, the sea anemone benefits from the presence of

Directions: In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will find alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also find questions about a particular section of the passage, or about the entire passage. These questions will be identified either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.PassageOn the Road AgainWe drive across the country the way most people might go from home to work and (1)back again to home. I guess you could call us nomads, except for the fact that our trips have become (2)fairly regular, mostly to Las Vegas, Nevada, (3)thanback to New York, our home for the past 35 years.My husband and I are retired high school teachers, which means that we have plenty of time (4)to travel. Three of our five children now live west of the Mississippi River. All of our grandchildren live in New York, and we have two large dogs. Therefore, staying in Las Vegas for more than three consecutive weeks is generally (5)enjoyable. And so, we find ourselves back on the road time and time again.Las Vegas (6)had becomeour sunshine sanctuary; we have become completely fed up with New York’s cold and gloomy winters and are determined to spend as much timeas possible in the (7)warm sunnyWest. Moreover, we have extended family in Nevada, Arizona, Colorado, and California, so vacationing in Las Vegas makes a lot of sense for us.1.(8)So we have two adopted (9)dogs, both of which areshelter mutts, flying is not an option; we want the dogs with us and we want to avoid paying boarding fees.2.And so, here we are, for the second time this month, trekking home with our dogs in our extended-cab truck.3.Hunter, a lab and spaniel mix, fills his limited space on the back bench seat, and Lizzie, our elderly pooch, lyingon her special blanket on the floor.4.They are quiet; they know the drill.5.Every few hours they get to jump out of the truck and sniff out the newest stop.(11)Thus far, we(12)have pastthe Hoover Dam, climbed the mountains of Flagstaff, Arizona, crossed the high deserts of New Mexico and the Texas panhandle, paid (13) our toll’s in Oklahoma, and looped around St. Louis, Missouri. After 26 hours on the road, we are a mere seven hours from home; this will be one of our fastest trips, thanks to pre-packed turkey sandwiches, fewer stops for gas, good weather, and audio books.The landscape in Missouri is surprisingly snow-free for the month of January, but the sky is becoming predictably thick with gray clouds. I’m mentally preparing myself fora sunless New York sky during our week at home.14 But that’s okay; it will just reinforce for me the purpose of getting right back on the road in seven days to head back to sunny Las Vegas.Q. (11)For the sake of logic and coherence, Sentence 5 should be placed

Top Courses for ACTView all

Top Courses for ACT

The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?a)(ab)642b)(ab)643c)a642bd)a643be)ab642Correct answer is option 'E'. Can you explain this answer?
Question Description
The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?a)(ab)642b)(ab)643c)a642bd)a643be)ab642Correct answer is option 'E'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?a)(ab)642b)(ab)643c)a642bd)a643be)ab642Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?a)(ab)642b)(ab)643c)a642bd)a643be)ab642Correct answer is option 'E'. Can you explain this answer?.
Solutions for The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?a)(ab)642b)(ab)643c)a642bd)a643be)ab642Correct answer is option 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for ACT. Download more important topics, notes, lectures and mock test series for ACT Exam by signing up for free.
Here you can find the meaning of The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?a)(ab)642b)(ab)643c)a642bd)a643be)ab642Correct answer is option 'E'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?a)(ab)642b)(ab)643c)a642bd)a643be)ab642Correct answer is option 'E'. Can you explain this answer?, a detailed solution for The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?a)(ab)642b)(ab)643c)a642bd)a643be)ab642Correct answer is option 'E'. Can you explain this answer? has been provided alongside types of The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?a)(ab)642b)(ab)643c)a642bd)a643be)ab642Correct answer is option 'E'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The first and second terms of a geometric sequence are a and ab, in that order. What is the 643rd term of the sequence?a)(ab)642b)(ab)643c)a642bd)a643be)ab642Correct answer is option 'E'. Can you explain this answer? tests, examples and also practice ACT tests.
Explore Courses for ACT exam

Top Courses for ACT

Explore Courses
SaveJoin the Discussion on the App for FREE
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Get App
© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup