The sum of the first 7 terms of an AP is 49 and the sum of the first 17 terms is 289.
Find the sum of the first $n$ terms (general formula), then state $S_{n}$ for $n = 10$ .

Question

The sum of the first 7 terms of an AP is 49 and the sum of the first 17 terms is 289. Find the sum of the first n terms (general formula), then state S_n for n = 10.

Accepted Answer

100. S_7 = 7/2(2a+6d) = 49 => a+3d=7. S_17 = 17/2(2a+16d)=289 => a+8d=17. Subtract: 5d=10 => d=2, a=1. S_n = n/2[2+2(n-1)] = n^2. S_10 = 100.

The sum of the first 7 terms of an AP is 49 and the sum of the first 17 terms is 289.
Find the sum of the first $n$ terms (general formula), then state $S_{n}$ for $n = 10$ .

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More Class 10 Sum of n Terms of an AP practice

The sum of the first 7 terms of an AP is 49 and the sum of the first 17 terms is 289.Find the sum of the first n terms (general formula), then state Sn​ for n=10.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Sum of n Terms of an AP practice

The sum of the first 7 terms of an AP is 49 and the sum of the first 17 terms is 289.
Find the sum of the first $n$ terms (general formula), then state $S_{n}$ for $n = 10$ .