Question

Find the sum of the first 15 terms of an A. P. whose nth term is given by (see figure Q.5-(i) ).

Answer 1

Given,

(i) nth term of an AP : 3 + 4n
Let us find out value of $a_{1}$

n = 1

$a_{1}$ = 3 + 4(1)

a = 3 + 4

a = 7


To find out 15th term, let n = 15

So, = 3 + 4(15)

= 3 + 60

= 63


Now,
Putting the values in the formula we get,

$S_{n} = \frac{n}{2}(a + l)$
where l = last term (i.e. 63 here)

$S_{15} = \frac{15}{2}(7 + 63) \\ \\ S_{15} = \frac{15}{2}(70) \\ \\ S_{15} = \frac{15}{2} × 70 \\ \\ S_{15} = 15 × 35 \\ \\ \bf S_{15} = 525$

Hope it helps! ;))