1.

If the sum of 8th term of an ap is 64 and the sum of 19 terms is 361 find the sum of n terms

Answer»

S8= 64
8/2 (2A+7d)=64
4(2a+7d)=64
2a+7d=16
2a=16-7d
a=16-7d/2------- (1)

S19= 361
19/2(2a+ 18d)=361
2a+18d=361×2/19
2a+18d= 38
putting equation 1 here,

2×16-7d/2 +18d= 38
32-14d/2+18d=38
16-7d+18d=38
11d= 38-16
d= 22/11
d=2

putting d=2 in eq.1

a=16-7d/2
a=16-14/2
a=1

Sn= n/2{2a+(n-1)d}
Sn=n/2{2×1+(n-1)×2}
Sn=n/2{2+(n-1)2}
Sn=n(1+n-1)
Sn= n^2


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