Question

find the number of terms of the AP -12, -9, -6 ...... , 21. If 1 is added to each term of this AP, then find the sum of all the terms of the AP thus obtained.

Answer 1

I have written it by myself please mark it as the brainllist if it will help you please say thanks for this answer too. . . . . . . . .

Answer 2

Answer:

$S_{12} = 66$

Step-by-step explanation:

To find the number of terms in the AP

-12, -9, -6 ...... , 21

here a=-12

d=3

let us find which term is 21,from the formula

$a_n = a + (n - 1)d \\ \\ 21 = - 12 + (n - 1)3 \\ \\ 21 + 12 = 3(n - 1) \\ \\ 33 = 3(n - 1) \\ \\ 11 = n - 1 \\ \\ n = 12$

so,there are 12 terms in the AP.

If 1 is added to each term of this AP,

Now new A.P. be -11,-8,...,22

n=12

a=-11

d=3

then find the sum of all the terms of the AP thus obtained

$S_n = \frac{n}{2} (2a + (n - 1)d) \\ \\ S_{12} = \frac{12}{2} ( - 22 + 11 \times 3) \\ \\ = 6( - 22 + 33) \\ \\ = 6 \times 11 \\ \\ S_{12} = 66$

Hope it helps you.