Question

the sum of first 7term of an ap is 63 and sum of its next 7 term 161 find its 28term

Answer 1

sum7 = 63
7/2 ( 2a + 6d) = 63

On solving the eq. will come like a+ 3d=9    .......eq 1

sum14 - sum7 = 161
sum14 - 63 = 161
sum14 = 224

14/2(2a + 13d) = 32
On solving , 2a + 13d =32     ......eq2

Now solve it simultaneously

eq2 - eq1

                          2a + 13d = 32
(a + 3d = 9)*2  = 2a + 6d = 18
                          -_____________
                                 7d= 14
                                   d=2

On putting the value of d,

a+3d = 9
a + 6 = 9
a = 3

term28 = a+ 27d
           = 3 + 27*2
           = 3 + 54
           = 57


Hope it helps  :)