Question

please answer this question ​

Answer 1

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Refer to the attachment.....☺️

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Answer 2

Answer:

(n*n) = (n^2)

Step-by-step explanation:

Given

S 7 =49 and S 17 =289

By using S n= n/2 * [2a+(n−1)d] we have,

S 7 = 7/2* [2a+(7−1)d]=49

⇒49=7/2 [2a+(7−1)d]

⇒49= 7/2 * (2a+6d)

⇒7=a+3d

⇒a+3d=7...................(i)

S 17 = 17/2 *[2a+(17−1)d]=289

⇒289= 17/2* [2a+(17−1)d]

⇒289= 17/2 *(2a+16d)

⇒17=a+8d

⇒a+8d=17......................(ii)

Substituting (i) from (ii), we get

5d=10 or d=2

From equation (i),

a+3(2)=7

a+6=7 or a=1

S n= n/2*[2(1)+(n−1)2]

= n/2 [2+(n−1)2]

= n/2(2+2n−2)= n^2= ( n*n)