Question

If
3+5+7+9... up to n terms =288,then n = ?

Answer 1

Answer:

Clearly , 5-3=2

And 7-5=2

Therefore the sequence.forms an AP

a or T1=3

d=2

Sn=n/2{2a+(n-1)d}=288

Or,

n/2{2(3)+(n-1)2}=288

Or,n/2{6+2n-2}=288

Or,n/2×2{3 +n - 1}=288

Or,n{2+n}=288

Or,2n +n^2=288

Or,n^2+2n-288=0

Or,n^2+18n-16n-288=0(middle term split)

Or,n(n+18)-16(n+18)=0

Or,(n+18)(n-16)=0

Therefore n+18=0 =>n=-18( term cannot be negative so not possible)

=>n-16=0=>n=16(Ans)