Math, asked by NazzNaser9840, 11 months ago

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.

Answers

Answered by nain31
9
 \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}}
Answered by akshat4228
4

Step-by-step explanation:

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

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