Question

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

Answer 1

$\bold{FOR \: GIVEN \: AP}$

First term a = -12

Common difference = 3

last term = l

So, to find number of terms

$\huge \boxed{l = a + (n -1)d}$

$\mathsf{21 = -12 + (n -1)3}$

$\mathsf{21 + 12= (n -1)3}$

$\mathsf{33= 3n - 3}$

$\mathsf{33 + 3= 3n }$

$\mathsf{36 = 3n }$

$\mathsf{\dfrac{36}{3} = n }$

$\mathsf{12 = n}$

So, AP have 12 terms.

$\bold{ACCORDING \: TO \: QUESTION}$

1 is added to each term so, new Ap will be

-12 + 1 = 11, -9 + 1 = 8 ,-6 + 1 = 5..........,21- 1 = 5.

First term $a_2$ = - 12 + 1

Common difference $d_2$ = 3

So,

$\huge \boxed{S_n = \dfrac{1}{2} (2a + (n-1)d)}$

$\mathsf{S_{12}= \dfrac{1}{2} (2 \times 11 + (12 -1) \times 3}$

$\mathsf{S_{12} = \dfrac{1}{2} (22 + 11 \times 3)}$

$\mathsf{S_{12} = \dfrac{1}{2} (22 + 33)}$

$\mathsf{S_{12} = \dfrac{1}{2} \times 55}$

$\huge \boxed{\mathsf{S_{12} = 27.5}}$

Answer 2

Step-by-step explanation:

s12=27.9................