Question

if tn = 3 + 4n then find the a.P. And hence find the sum of its first 15 terms.

Answer 1

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Answer 2

Given:

tn = 3 + 4n.

To find:

The A.P. and sum of its first 15 terms.

Solution:

As given,

The nth term is given by:

tn = 3 + 4n

On putting n = 1

t1 = 7

Similarly,

on putting n = 2

t2 = 3 + 4(2) = 11

when n = 3

t3 = 3 + 4(3) = 15

Hence, the A.P. is 7, 11, 15...

Now,

first term or a = 7

the common difference = 2nd term - 1st term = 11-7 = 4

So,

The sum of n terms

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

The sum of 15 terms

$= \frac{15}{2}[ 2(7) + (15 - 1)4 ]$

(as n = 15)

$= \frac{15}{2} (14 + 56)$

$= \frac{15}{2} (70)$

$= 15 \times 35$

$= 525$

Hence, the sum of 15 terms is 525.