Q.

The sum of first 7 terms of an 𝐴𝑃 is 63 and the sum of its next 7 terms is161. Find the 28𝑡ℎ term of this 𝐴. 𝑃.

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Detailed Solution

Given that, 

The sum of first 7 terms of an 𝐴𝑃 is 63 

The sum of its next 7 terms is 161 

Now we have to find that the 28𝑡ℎ term of this 𝐴. 𝑃 

Here, 𝑆₇ = 63 and 𝑛 = 7 The sum of terms in an 𝐴. 𝑃.

S=n2(2a+(n1)d)63=72(2a+(71)d)63=72(2a+6d)        

63=7a+21d                        9=a+3d                               a=93d(i)                         Also, S14=63+161                S14=224 n=14                 224=142(2a+(141)d)    224=7(2a+13d)                 224=7(2(9 3d)13d)      32=186d+13d                32=18+7d                          7d=14                                  d=2                                       

From (i), a=96 

 Now, a28=a+27d

=3+27(2)   =3+54        =57              a28=57   

Hence, the 28𝑡ℎ term of this 𝐴. 𝑃. is 57

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