What is the sum of the first 8 terms of the arithmetic progression whose first term is $3$ and common difference is $5$ ?

easy MCQ 1 mark Class 11 · Mathematics · Sequences and Series

Answer

164

The correct answer is 164 — Answer: $164$ .

Step-by-step solution

Let the first term be $a = 3$ and common difference $d = 5$ .
Use the formula for the sum of first $n$ terms: $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ .
Substitute $n = 8$ , $a = 3$ , $d = 5$ : $S_{8} = \frac{8}{2} [2 \cdot 3 + (8 - 1) \cdot 5]$ .
Compute inside brackets: $2 c d o t 3 = 6$ , $(8 - 1) c d o t 5 = 35$ , so $6 + 35 = 41$ .
Thus $S_{8} = 4 \times 41 = 164$ .
Answer: $164$ .

Common mistake: Forgetting to multiply by

\frac{n}{2}

or mixing up the formula for

S_{n}

Concept tested: Arithmetic progression sum