Question

if the sum of first 7 term of an arithmetic progression is 49 and that of 17 term is 289 find the sum of n terms

Answer 1

sum of n terms = n²

Step-by-step explanation:

first term = a

common difference = d

7th term = a +  6d

Sum of 7 terms =  (7/2)(a + a + 6d)  = 49

=> a + 3d = 7

17th Term = a + 16d

Sum of 17 Terms = (17/2)(a + a + 16d)  = 289

=> a + 8d = 17

=> 5d= 10

=> d  = 2

a = 1

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

= n( 1 + n - 1)

= n²

sum of n terms = n²

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