Sequences & Series
Geometric Progression (GP)
Grade 11
Question:
<p>Let {a,, }%=1 be a sequence such that a, = 1, az = 1 and dy42 = 2an41 + Gp for all n > 1. Then the 4, value of 47> 3 in is equal to —_—_— [EE (Main) 2021] 26. The 4% term of G.P. is 500 and its common ratio is —, me N . Let S,, denote the sum of the first n m n=</p>
Step-by-Step Solution
Key Concept: Notice the hidden common ratio first. Once the ratio is pinned down, the rest of the progression falls into place very quickly.
Notice that the real unlock is the common ratio. A clever move here is to write consecutive terms in powers of the ratio and then use the given condition to collapse the algebra. Now, we invoke the power of the G.P. identities for the nth term and the sum, simplify patiently, and verify that the final answer is \(5\).
Correct Answer: 5