Question

finnnnnnnnnnnnnnddddddddddddddddddddddd​

Answer 1

$\bold{ANSWER }$

◼${Number \: of \: terms = 30}$

◼${Sum \: of \: these\: 30 \: terms =3435}$

$\bold{SOLUTION}$

Given,

First term a = 13

Common difference d = 7

last term l = 216

Since,

$t_n = a + (n -1) d$

On placing values,

216 = 13 + (n - 1) × 7

216 = 13 +7n - 7

216 = 13- 7 + 7n

216 = 6 + 7n

216 - 6 = 7n

210 = 7n

$\frac{210}{7} = n$

n= 30

So ,the number of terms are 30 .

To find the sum of these 30 terms

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

$S_n = \frac{30}{2} \times (2 \times 13 + (30 -1) \times 7)$

$S_n = 15 \times (2 \times 13 + 29 \times 7)$

$S_n = 15 \times (26 + 29 \times 7)$

$S_n = 15 \times (26 + 29 \times 7)$

$S_n = 15 \times (26 + 203 )$

$S_n = 15 \times 229$

$S_n = 3435$

So ,the sum of 30 terms is 3435.