If the fifth term of a GP is 81 and first term is 16, what will be the 4th term of the GP?a)36b)18c)54d)24Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Given:
The fifth term of a GP is 81
The first term is 16

To find:
The fourth term of the GP

Formula for the nth term of a geometric progression (GP):
$$a_n = a_1 \times r^{(n-1)}$$

where $a_n$ is the nth term,
$a_1$ is the first term,
r is the common ratio,
and n is the position of the term.

Let's solve the problem step by step:

1. Finding the common ratio (r):
We are given the fifth term (81) and the first term (16).
Using the formula, we can substitute these values and find the common ratio:
$$81 = 16 \times r^{(5-1)}$$
$$81 = 16 \times r^4$$
Dividing both sides by 16:
$$5.06 = r^4$$
Taking the fourth root of both sides:
$$r = \sqrt[4]{5.06}$$
$$r \approx 1.68$$

2. Finding the fourth term (a4):
Now that we have the common ratio, we can use the formula to find the fourth term (a4):
$$a_4 = 16 \times 1.68^{(4-1)}$$
$$a_4 = 16 \times 1.68^3$$
$$a_4 \approx 54$$

Therefore, the fourth term of the geometric progression is approximately 54. Hence, the correct answer is option C.

Similar Quant Doubts

If the fifth term of a GP is 81 and first term is 16, what will be the 4thterm of the GP?

A clock is set right at 5 AM.The clock losses 16 min in 24 h.what will be the night time when the clock indicates 10 pm on the 4th day?

The first term of an AP = the common ratio of a GP and the first term of the GP = common difference of the AP. If the sum of the first two terms of the GP is equal to the sum of the first 2 terms of the AP, then the ratio of the first term of the GP to the first term of an AP is

Find the second term of an AP if the sum of its first five even terms is equal to 15 and the sum of the first three terms is equal to 3.

Top Courses for Quant

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company