Question

Find the 7th term of ap whose sum of n terms is 3n2 5n

Answer 1

Hi,

44

Explanation:

I suppose sum of n terms is 3n²+5n

Let's assume a the first term, r the commun difference .

`\displaystyle \sum_(i=1)^n\ (a+(i-1)r)=3n^2+5n\\\\n*a+r*\sum_(j=0)^(n-1)\ j=3n^2+5n\\\\na+r*(n*(n-1))/(2) =3n^2+5n\\(r)/(2) *n^2-r*n+a*n=3n^2+5n\\\\(r)/(2) =3 \Longrightarrow\ r=6\\\\a-(r)/(2) =5 \Longrightarrow\ a-3=5 \Longrightarrow\ a=8\\\\7^(th)\ term\ is\ a+6*r=8+6*6=\boxed{44}\\`