The third term of a GP is 12 and the sixth term is 96. The first term is:

Question

In the sequence 1, 3, 5, 7, ..., k, ..., 57, the sum of the numbers up to k, excluding k, is equal to the sum of the numbers from k up to 57, also excluding k. What is k?

Answer 1

Step 1: \(\dfrac{ar^5}{ar^2} = \dfrac{96}{12} = 8 \Rightarrow r^3 = 8 \Rightarrow r = 2\).
Step 2: \(ar^2 = 12 \Rightarrow a\times4 = 12 \Rightarrow a = 3\).

Quick Tip: Divide two term-equations to eliminate \(a\) and solve for the ratio \(r\) first.

The third term of a GP is 12 and the sixth term is 96. The first term is:

The Correct Option is A

Solution and Explanation

Top Questions on Progressions (AP & GP)

Questions Asked in ATMA exam