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# In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms. - CBSE Class 10 - Mathematics

ConceptSum of First n Terms of an AP

#### Question

In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.

#### Solution

S_5+ S_7= 167 and S 235_10=235

Now S_n=n/2{2a+(n-1)d}

S_5+S_7=167

5/2{2a+4d}+7/2{2a+6d}=167

12a+31d=167.......(i)

alsoS_10=235

10/2{2a+9d}=235

2a+9d=47 .........(ii)

Multiplying equation (2) by 6, we get

12a + 54d =282 .....(3)

(-)12a+31d=167

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23d=115

therefore d=5

Substituting value of d in (2), we have

2a+9(5)=47

2a+45= 47

2a=2

a=1

Thus, the given A.P. is 1, 6, 11, 16,..........

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Solution In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms. Concept: Sum of First n Terms of an AP.
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