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If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first ‘n terms.

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If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first ‘n terms.

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S7 = 49, S17 = 289, S11 =?

∴ 2a + 16d = 34 …………. (ii)

10d = 20 

∴ d=2 

Substituting the value of d in equation (i), we have 

2a + 6d = 14 

2a + 6 × 2 = 14 

2a + 12 = 14 

2a = 14 – 12 

2a = 2

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