If the sum of a certain number of terms of the AP 27, 24, 21, 18, …. is –30, find the last term.

Question

Philoid · Accepted Answer

To Find: Last term of the AP.

Let the number of terms be n.

⇒n[54 - 3n + 3] = - 60

⇒3n² - 57n - 60 = 0

Either n = 20 or n = - 1 (n cannot be negative)

Therefore n = 20

Also,

, where l is the last term.

⇒ - 30 = 270 + 10l

⇒l = - 30

The last term is - 30.