Question

Sum of 2nd term to 15 th term of an as is 518.find the sum of first 16 terms of this sequence

Answer 1

Given:

S16= 112

Sum of next 14 terms is= 518

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

S16=16/2[2a+(16-1)d]

112=16/2[2a+15d]

112= 8 [2a+15d]

112/8 =2a+15d

14=2a+15d…………………….. (1)

Sum of next 14 terms is 518.

Sum of first (16+14) terms(S30) = 112+518

S30 = 630

S30=30/2[2a+(30-1)d]

630=30/2[2a+29d]

630 = 15[2a+29d]

630/15 = [2a+29d]

42=2a+29d ……………………...(2)

Subtracting eq (1) from eq (2)

42 = 2a+29d

14 = 2a+15d

(-) (-) (-)

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28 = 14d

d= 28/14

d=2

Substitute the value of d in eq (1)

14=2a+15d

14 = 2a + 15(2)

14 = 2a + 30

14-30 = 2a

2a= -16

a= -16/2

a= -8

If ‘a’ is the first term and 'd’ is a common difference then the Arithmetic progression is

a, a+d, a+2d, a+3d ,……..

-8, -6, -4,-2,........

Hence , the Arithmetic progression is 8, -6, -4,-2,........