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Sequence and Series

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Question : 49 of 86

Marks: +1, -0

If the 10th term of an A.P. is twice the 4th term and the 23rd term is 'k' times the 8th term, then the value of 'k'

2.5
3
3.5
4

Solution:

Concept:

Use the formula for the

n

th term of an arithmetic progression:

T_n = a + (n-1)d

.

Explanation:

Let the first term be

a

and common difference

d

.

Given:

T_{10} = 2 \cdot T_4

.

So

a + 9d = 2(a + 3d)

.

This gives

a + 9d = 2a + 6d

→

3d = a

→

a = 3d

.

Now given:

T_{23} = k \cdot T_8

.

So

a + 22d = k (a + 7d)

.

Substitute

a = 3d

:

3d + 22d = k (3d + 7d)

→

25d = k (10d)

.

Assuming

d \neq 0

, cancel

d

:

25 = 10k

→

k = \frac{25}{10} = 2.5

.

Answer:

k = 2.5

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