Question

the first and the last term of an AP are 10 and 361 respectively. if its common difference is 9 then find the number of terms and their total sum ?

Answer 1

Given, First term a = 10.

Last term an = l = 361.

Common difference, d = 9.

Now,

We know that nth term of an AP an = a + (n - 1) * d

⇒ 361 = 10 + (n - 1) * 9

⇒ 361 - 10 = 9n - 9

⇒ 351 = 9n - 9

⇒ 360 = 9n

⇒ n = 40.

We know that Sum = (n/2)[a + l]

⇒ (40/2)[10 + 361]

⇒ 20[371]

⇒ 7420.

Therefore:

⇒ Number of terms = 40.

⇒ Sum = 7420.

Hope it helps!

Answer 2

First(a) =10 and C.D(d)=9

a+(n-1)d=361

10+(n-1)9=361

10+9n-9=361

9n+1=361

9n=361-1

n=360/9

n=40

Now,

Sum of nth term=n/2[2a+(n-1)d]

=40/2[2*10+(40-1)9]

=20[20+39*9]

=20(20+351)

=20*371

=7420