Question

How many terms of an AP 54,51,48.... be taken ao that their sum is 513? explain double answer.

Answer 1

a = 54

d = -3

Sn = 513

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

513 = n/2( 108 + 3 -3n)

1026 = 111n - 3n^2

n^2 -37n +342 = 0

on solving, we get

n= 18 , n=19

We are getting here 2 values , both positive so , Both are applicable here

Answer 2

a=54
d=-3
an=513

an = n/2(2a+(n-1)d)
513 = n/2(2×54 +(n-1)-3)

1026 = n(108 -3n+3)
1026=n(111-3n)
3n²-111n+1026=0
3(n²-37n+342)=0
n²-18n-19n+342=0
n(n-18) + 19n(n-18) =0

(n-18)(n-19) =0

so n = 18 or 19