Question

The sum of \(10\) terms of A.P. \(:2,7,12,.........\) is

• A. 340
• B. 345
• C. 240
• D. 245

Answer 1

The Correct Option is D

To solve the problem, we need to find the sum of the first 10 terms of the Arithmetic Progression (A.P.): 2, 7, 12, ...

1. Identifying the First Term and Common Difference:
The first term $a = 2$
The common difference $d = 7 - 2 = 5$

2. Using the Formula for Sum of First n Terms of A.P.:
The formula is:
$ S_n = \frac{n}{2} \left[2a + (n - 1)d \right] $
Substituting the known values ($n = 10$, $a = 2$, $d = 5$):
$ S_{10} = \frac{10}{2} \left[2(2) + (10 - 1)(5) \right] $
$ S_{10} = 5 \left[4 + 45 \right] $
$ S_{10} = 5 \times 49 = 245 $

Final Answer:
The sum of the first 10 terms is $ {245} $