Question

The 8th term of an A.P. is 23 and the 11th term of the A.P. is thrice of its 3rd term. Find the sum of first 10th term.​

Answer 1

EXPLANATION.

• GIVEN

8th term of an Ap = 23

11th term of an Ap is thrice of its 3rd term.

To find sum of its first 10th term.

According to the question,

8th term of an Ap = 23

a + 7d = 23 .......(1)

11th term of an Ap is thrice of its 3rd term.

a + 10d = 3 ( a + 2d )

a + 10d = 3a + 6d

- 2a + 4d = 0

-2a = -4d

a = 2d ......(2)

Put the value of a = 2d in equation (1)

we get,

2d + 7d = 23

9d = 23

d = 23/9

Therefore,

a = 2 X 23 / 9

a = 46 / 9

sum of nth term of an Ap

$\bigstar\boxed{\orange{\bold{s_{n} \: = \frac{n}{2} (2a \: + (n - 1)d)}}}$

$\bold{s_{10} \: = \frac{10}{2} (2 \times \frac{46}{9} + (9 \times \frac{46}{9} )}$

$\bold{s_{10} \: = 5( \frac{92}{9} + 23)}$

$\bold{s_{10} = \: 5( \frac{92 + 207}{9} )}$

$\bold{s_{10} \: = 5( \frac{299}{9} )}$

$\bold{s_{10} \: = \frac{1495}{9}}$

Therefore,

sum of first 10th term of an Ap = 1495/9