Class 10 Exam > Class 10 Notes > Mathematics Class 10 ICSE > Worksheet: Geometric Progression
Worksheet: Geometric Progression | Mathematics Class 10 ICSE PDF Download
Section A — Very Short Answer
Q1. Find the common ratio of the sequence 5, 15, 45, ...
Q2. Find the 4th term of the G.P. 3, 6, 12, ...
Q3. The second term of a G.P. is 12 and r = 1/3. Find the first term.
Q4. Find the geometric mean between 4 and 25.
Q5. If a = 81 and r = 1/3, find t5.
Section B — Short Answer
Q6. Find the 8th term of the G.P. 2/3, 4/3, 8/3, ...
Q7. In the G.P. 5, 5/2, 5/4, ... which term equals 0.3125?
Q8. Find the sum of first 6 terms of the G.P. 3, −6, 12, −24, ...
Q9. Find the sum to infinity of the G.P. 5 + 5/2 + 5/4 + 5/8 + ...
Q10. Insert three geometric means between 2 and 162. (So make a G.P. with 5 terms: 2, G1, G2, G3, 162.)
Section C — Long Answer
Q11. The 4th term of a G.P. is 54 and the 7th term is 1458. Find the first term a, the common ratio r, and the sum of the first 8 terms.
Q12. A sequence is 486, 162, 54, ... and continues until a term equals 2/3.
Find (i) how many terms are there, and
(ii) the total (sum) of all those terms.
Q13. The sum to infinity of a G.P. is 8 and its second term is 2. Find the first term, the common ratio, and the sum of the first 6 terms.
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FAQs on Worksheet: Geometric Progression - Mathematics Class 10 ICSE
| 1. What is a geometric progression? |  |
Ans. A geometric progression (GP) is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 2, 6, 18, 54, the common ratio is 3.
| 2. How do you find the nth term of a geometric progression? | |
Ans. The nth term of a geometric progression can be found using the formula: aₙ = a₁ × r^(n-1), where a₁ is the first term, r is the common ratio, and n is the term number. For example, if a₁ = 3 and r = 2, the 5th term would be a₅ = 3 × 2^(5-1) = 3 × 16 = 48.
| 3. What is the sum of the first n terms of a geometric progression? | |
Ans. The sum of the first n terms (Sₙ) of a geometric progression is given by the formula: Sₙ = a₁ × (1 - rⁿ) / (1 - r) for r ≠ 1, where a₁ is the first term and r is the common ratio. For instance, if a₁ = 5 and r = 3, the sum of the first 4 terms would be S₄ = 5 × (1 - 3⁴) / (1 - 3) = 5 × (1 - 81) / (-2) = 5 × (-80) / (-2) = 200.
| 4. Can a geometric progression have a negative common ratio? | |
Ans. Yes, a geometric progression can have a negative common ratio. This results in alternating positive and negative terms. For example, if the first term is 4 and the common ratio is -2, the sequence would be 4, -8, 16, -32, and so on.
| 5. How can geometric progressions be applied in real life? | |
Ans. Geometric progressions can be found in various real-life scenarios, such as in finance (for calculating compound interest), biology (population growth), physics (radioactive decay), and computer science (algorithm efficiency). For instance, if an investment doubles every year, it represents a geometric progression where the common ratio is 2.
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