Question

The first term of an A.P. is 5, the last term is 45 and the sum of its terms is 1000. Find the number of terms and the common difference of the A.P.

Answer 1

First term a = 5

Last term l = 45

Sum of terms = 1000

Let there be n terms in this A.P.

Now, sum of first n terms = ${\displaystyle \frac{n}{2}[a+l]}$

${\displaystyle \Rightarrow 1000=\frac{n}{2}[5+45]}$

${\displaystyle \Rightarrow }$ 2000 = n × 50

${\displaystyle \Rightarrow }$ n = 40

l = a + (n – 1)d

${\displaystyle \Rightarrow }$ 45 = 5 + (40 – 1)d

${\displaystyle \Rightarrow }$ 40 = 39d

${\displaystyle \Rightarrow d=\frac{40}{39}}$

Hence, number of terms are 40 and common difference is ${\displaystyle \frac{40}{39}}$.