Question

if the sum of an AP is 49 and that of first 17 terms is 289 find the sum of its n terms

Answer 1

HEYA!!!!!

Given,

Sum of first seven terms = 49

sum of seventeen terms = 289

then, Sum of first n terms = ?

49 = n/2 ( 2a + ( n-1) d )

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

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

2a + 6d = 49 × 2/7

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



S17 = 289

n/2 ( 2a + ( n-1) d ) = 289

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

2a +16d = 289 × 2/17

2a + 16d = 34 ----------(2)


from (1) & (2)

2a + 6d = 14

(+)-2a (+) - 16d = 34
----------------------
- 10 d = -20

d = 20/10

d = 2


Substitute d=2 in eq - (1)

2a + 6 ( 2) = 14

2a = 14-12

2a = 2

a = 2/2

a = 1


Sn = n/2 ( 2a + (n-1) d )

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

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

= n/2 × 2n

= n × n

Sn. = n^2 ...


HOPE THIS HELPS U. .