Question

if the sum of first 7 term of an ap is 489 and that of 17 terms is 289 find the sum of first n term
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Answer 1

Step-by-step explanation:

Now, sum of n terms = n{2a+(n-1)d}/2

So,sum of 7terms = 7{2a+(7-1)d/2

49 = 7{2a+6d}

7 = 2a+6d.................(1)

and,sum of 17 terms =17{2a+(17-1)d}

289 = 17{2a+16d}

17 = 2a+16d.....................(2)

subtract eq(2) from eq(1) ,we get

17-7 = 2a+16d-2a-6d

10 = 10d

d = 1

putting value of d in eq(1),we get

2a+6d = 7

2a+6 = 7

a = 1/2

So, sum of n terms = n{2×1/2+(n-1)1}/2

= n{1+n-1}/2

= n²/2