SSC CHSL 2023 PYQ — Question 69

The correct answer is option 4 i.e. 3.

Series: 9 + 9² + ... + 9⁽²ⁿ⁺¹⁾ = $\sum\limits_{k=1}^{(2n+1)}9^k$

9 ÷ 6 leaves a remainder of 3

9² = 81, and 81 ÷ 6 leaves a remainder of 3

9³ = 729, and 729 ÷ 6 leaves a remainder of 3

In general, 9^k ÷ 6 will always leave a remainder of 3 for any positive integer k

Sum of remainders = 3(2n + 1) = 6n + 3

(6n + 3)/6 → leaves a remainder of 3

Hence, the remainder is 3.