Question

In an A.P. given that the first term (a) = 54, the common difference
(d) = -3 and the nth term = 0, find n and the sum of first n terms of the A.P​

Answer 1

Answer:

n = 19

Sum of first n terms = 513.

Step-by-step explanation:

The nth term of an AP is:

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

Given:

a = 54

d = -3

Tₙ = 0

Compute the value of n as follows:

$T_{n}=a+(n-1)d\\0=54+(n-1)(-3)\\0=54-3(n-1)\\3(n-1)=54\\n-1=18\\n=19$

There are 19 terms in the AP.

The formula to compute the sum of n terms of an AP is:

$S=\frac{n}{2}[2a+(n-1)d]$

Compute the sum as follows:

$S=\frac{n}{2}[2a+(n-1)d]\\=\frac{19}{2}[(2\times54)+(19-1)(-3)]\\=\frac{19}{2}\times 54\\=513$

Thus, the sum of the first n terms is 513.