Question

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 1

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

Answer 2

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poodarvitan

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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

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poodarvitan

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ajmal64

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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