Find the sum of the first 10 terms of the arithmetic progression whose first term is $7$ and common difference is $4$ .

easy 1 mark Class 11 · Mathematics · Sequences and Series

Answer

250

The correct answer is 250 — Thus the required sum is $250$ .

Step-by-step solution

Use the formula for the sum of an arithmetic series $S_{n} = \frac{n}{2} (2 a + (n - 1) d)$ .
Substitute $n = 10$ , $a = 7$ and $d = 4$ to get $S_{10} = \frac{10}{2} (2 \cdot 7 + (10 - 1) \cdot 4) = 5 (14 + 36) = 5 \cdot 50 = 250$ .
Thus the required sum is $250$ .

Common mistake: Using

S_{n} = \frac{n}{2} (a_{1} + a_{n})

without finding

a_{n}

or miscomputing

d

Concept tested: Arithmetic series sum