Question

HEYA!!!

Sum of 7 terms is 49. Sum of 17 terms is 289. Then find the sum of n terms.


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Answer 1

I hope it will help.

Answer 2

Given that sum of 7 terms = 49.

We know that sum of 1st n terms of an AP sn = n/2(2a + (n - 1) * d)

                                                                     49 = 7/2(2a + (7 - 1) * d)

                                                                    49 *2 = 7(2a + 6d)

                                                                   98/7 = 2a + 6d

                                                                   14 = 2a + 6d   -------- (1)




Given that sum of 17 terms is 289.

a17 = n/2(2a + (n - 1) * d)

289 = 17/2(2a + (17 - 1) * d)

289 * 2 = 17(2a + 16d)

578/17 = 2a + 16d

34 = 2a + 16d   ---------- (2)


On solving (1) & (2), we get

2a + 16d = 34

2a + 6d = 14

-------------------------

        10d = 20

           d = 2


Substitute d = 2 in (1), we get

2a + 6d = 14

2a + 6(2) = 14

2a + 12 = 14

2a = 14 - 12

2a = 2

a = 1.


Now,


Sum of n terms = n/2(2a + (n - 1) * d)

                           = n/2(2(1) + (n - 1) * 2)

                           = n/2(2 + 2n - 2)

                           = n/2(2n)

                           = n^2.




Therefore the sum of n terms = n^2.



Hope this helps!