Question

If an AP,the sum of its first n terms is n^2 + 2n. Find its 18th term and nth term

Answer 1

Answer:

$T_{n}=a+(n-1)d$

$T_{18}=37$

Step-by-step explanation:

Given : The sum of its first n terms is $n^2 + 2n$

To find : The 18th term and nth term

Solution : In an A.P

The sum of its first n terms is $n^2 + 2n$

Sum of first term or first term is when n=1

$n^2 + 2n=1^2 + 2(1)=1+2=3$

i.e, a=3

Sum of two terms n=2

$n^2 + 2n=2^2 + 2(2)=4+4=8$

Sum of first two term is $a+a+d=2a+d$

$2a+d=8$

$2(3)+d=8$

$d=8-6$

$d=2$

Now, a=3 and d=2

Formula of nth term is $T_{n}=a+(n-1)d$

18th term is,

$T_{18}=3+(18-1)2$

$T_{18}=3+(17)2$

$T_{18}=3+34$

$T_{18}=37$

Therefore, 18th term is 37.