Question

Find the number of terms of the arithmetic progression 54,51,48,,,,so that their sum is 513

Answer 1

Hey sup!

As per the question,

a=54.
d=-3.
S(n)=513.
=>n/2{2a+(n-1)d}=513.
=>n/2{2*54+(n-1)-3=513.
=>n/2(108-3n+3)=513.
=>n(111-3n)=513*2.
=>111n-3n^2=1026.
=>111n-3n^2-1026=0.
=>-3(n^2-37n+342)=0.
=>n^2-37n+342=0/-3=0.
=>n^2 -18n-19n+342=0.
=>n(n-18)+19(n-18)=0.
=>(n-18)((n+19)=0.
We have got two roots.
We'll discard n+19 as it gives-ve value.

So, n-18=0.
n=18.

Hence number of terms will be 19 of AP 54,51,48 whose sum is 513.

Hope it helps.