Question

if the sum of 7 terms of an ap 49 and that of 17 terms is 289find the sum of n terms?

Answer 1

Here is your Answer

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S 7 = 7/2 [2a+(6)d]

49* 2/7 = 2a+6d

7*2 = 2a+6d

14 = 2a+6d........(1)

s17= 17/2 (2a+16d)

289*2/17 = 2a+16d

17*2 = 2a + 16d

34 = 2a + 16d .........(2)

subtracting eq. 2 from 1 we will get

20 = 10 d

so ,d = 2

putting d = 2 in eq. 1

14 = 2a + 6 * 2

14 = 2a + 12

14 - 12 = 2a

2a = 2

a = 1

sn= n/2 [2a+ (n-1)d]

=n/2[2+2(n)-2]

=n/2×(2n)

=n2

sn =n^2

so sum of first natural number = n^2
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