Question

The sum of 1st 7 term of an a.p. is 63 and the sum of its next 7term is 161 find 28th term of this a.p.

Answer 1

The sum of 1st 7 term of an a.p. is 63

so, a + (a+d) + (a+2d) + (a+3d) + (a+4d) + (a+5d) + (a+6d) = 63
7a + 21d = 63
7(a+3d) = 63
a+3d = 63/7
a+3d = 9
a = 9 - 3d..............(1)

the sum of its next 7term is 161

so, (a+7d) + (a+8d) + (a+9d) + (a+10d) + (a+11d) + (a+12d) + (a+13d) = 161
7a + 70d = 161
7(a+10d) = 161
a + 10d = 161/7
a + 10d = 23..............(2)

substitute (1) in (2)
9 - 3d + 10d = 23
7d = 23 - 9
7d = 14
d = 14/7
d = 2

substitute d in (1)
a = 9 - 3*2
a = 9-6
a = 3

28th term , t(n) = a + (n-1)d
n = 28
a = 3
d = 2

so, t(28) = 3 + (28-1)*2 = 3 + 27*2 = 3 + 54 = 57