Question

16 added to the sum of the first few term of the arithmetic sequence 9,11,13,.... gave 256. How many terms were added?

Answer 1

a=9 , d= 11-9 = 2

n = ?

Sn + 16 = n/2 { 2a+(n-1)d } +16 = 256

n/2 { 2a+(n-1)d } = 256-16

n/2 { 2a+(n-1)d } = 246

2an +. n(n-1)d = 246 ×2

2an +. n(n-1)d = 492

2×9 + n(n-1)×2 = 492

18 + n(n-1) ×2 = 492

n(n-1) ×2 = 492 -18

n(n-1) = 474/2

n(n-1) = 237

n²-n -237 = 0

on comparing this eq with

standard form of quadratic equation

ax²+bx +c =0

we get

a= 1 ,b = -1 and c = -237

D= b²-4ac = -1² -4×1 ×- 237 = 1 + 948

D= 949

x= -b +-√D /2a = 1+- √949 /2

x = 1+- 30.8 /2

when +

x= 1+ 30.8 /2 = 31.8/2 = 15.9

when -

x= 1- 30.8 /2 = -29.8/2 = -14.9