Question

Sum of the series 2 + 6 + 18 + 54 + .... + 4374 is:

• A. 6550
• B. 6560
• C. 6660
• D. 6650

Hint:

For geometric series, use the sum formula and find the number of terms by solving for the last term in the sequence.

Answer 1

The Correct Option is B

This is a geometric series where the first term \( a = 2 \) and the common ratio \( r = 3 \).
The sum of the first \( n \) terms of a geometric series is given by the formula: \[ S_n = \frac{a(r^n - 1)}{r - 1} \] To find the sum, we need to first determine the number of terms in the series.
Given the last term \( T_n = 4374 \), we can find \( n \) using the formula: \[ T_n = a r^{n-1} \quad \Rightarrow \quad 4374 = 2 \times 3^{n-1} \] Solving for \( n \), we get \( n = 9 \).
Now, we can calculate the sum of the first 9 terms: \[ S_9 = \frac{2(3^9 - 1)}{3 - 1} = 6560 \]