NumericalModerate3 marks
The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series.
Topic: Geometric progression
Previous-year question practice database
Answer
Exam answer
a = 2
Explanation
Let a be the first term and r the common ratio and T4 = 16, T7 = 128 ∴ a r4 – 1 = 16 and a r7 – 1 = 128 a r3 = 16 a r6 = 128 a r6 a r3 = ∴ r3 = 8 = 23 ∴ r = 2 ar3 = 16 ⇒ a × 23 = 16 ∴ a = 2
More from Geometric Progression
Assertion (A): The 9th term of a Geometric Progression (G.P.) 6, −12, 24, −48, ... is a positive term.
Reason (R): The value of (−2)⁸ is always positive.
(A) is true and (R) is false.
(A) is false and (R) is true.
Both (A) and (R) are true and (R) is the correct explanation of (A).
Both (A) and (R) are true but (R) is not the correct explanation of (A).2026common ratio2026first term2026the value of 'n'2025hence find the sum of the 'n' terms of the G.P.2025Find the nth term of this G.P. in terms of n.2024