## give 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​

Question

give 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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1 month 2021-08-14T18:01:08+00:00 2 Answers 0 views 0

1. ### Solution :

Firstly,we know that formula of the sum of an A.P;

• a is the first term.
• d is the common difference.
• n is the term of an A.P.

### &

∴ Subtracting equation (1) & equation (2),we get;

Putting the value of d in equation (1),we get;

Now;

Thus;

The sum of first n terms will be n² .

2. $$\large\tt\purple{Sn=\frac{n}{2}(2a+(n-1)d)}$$

$$\large\tt\purple{S7=\frac{7}{2}(2a+(7-1)d)}$$

$$\large\tt\purple{49=\frac{7}{2}(2a+6d)}$$

$$\large\tt\purple{49=7(a+3d)}$$

$$\large\tt\purple{7=7-3d…….(1)}$$

$$\large\tt\purple{S14=\frac{17}{2}(2a+(17-1)d)}$$

$$\large\tt\purple{289=\frac{17}{2}(2a+16d)}$$

$$\large\tt\purple{289=17(a+8d)}$$

$$\large\tt\purple{17=a+8d}$$

$$\large\tt\purple{17=7-3d+8d}$$

$$\large\tt\purple{5d=10}$$

$$\large\tt\purple{d=2}$$

$$\large\tt\purple{a=7-3×2}$$

$$\large\tt\purple{a=1}$$

$$\large\tt\purple{Sn=\frac{n}{2}(2a+(n-1)d)}$$

$$\large\tt\purple{\frac{n}{2}(2(1)+(n-1)(2))}$$

$$\large\tt\purple{\frac{n}{2}(2+2n-2}$$

$$\large{\boxed{\tt{\purple{{n}^{2}}}}}$$