Quantitative Reasoning

Progression & Series

Easy

In arithmetic progression(A.P.), the first term is 7 and the 6th term is 22. The sum of the first 10 terms of A.P. is:

215

205

410

200

✅ Correct Option: 2

The first term is $a_1 = 7$ and the 6th term is $a_6 = 22$ .

The general term of an arithmetic progression is:

$a_n = a_1 + (n - 1) \times d$

For the 6th term:

$a_6 = a_1 + (6 - 1) \times d$

$22 = 7 + 5d$

$15 = 5d$

$d = 3$

The sum of the first $n$ terms of an arithmetic progression is:

$S_n = \frac{n}{2} \times [2a_1 + (n - 1) \times d]$

For the first 10 terms with $a_1 = 7$ and $d = 3$ :

$S_{10} = \frac{10}{2} \times [2(7) + (10 - 1) \times 3]$

$S_{10} = 5 \times [14 + 9 \times 3]$

$S_{10} = 5 \times [14 + 27]$

$S_{10} = 5 \times 41$

$S_{10} = 205$

Therefore, the sum of the first 10 terms is $205$ .

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In arithmetic progression(A.P.), the first term is 7 and the 6th term is 22. The sum of the first 10 terms of A.P. is:

Solution

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