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Sequence and Series

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Question : 74 of 86

Marks: +1, -0

The value of

{K},

for which the terms

7 {K}+3,4 {K}-5,

2 {K}+10

are in A.P., is

$13$
$-23$
$- 13$
$23$

Solution:

Concept:

For three terms in arithmetic progression (AP), the sum of first and third equals twice the middle term.

Explanation:

Given terms:

7K+3

,

4K-5

,

2K+10

.

Condition for AP:

2(\text{middle}) = \text{first} + \text{third}

.

Thus,

2(4K-5) = (7K+3) + (2K+10)

.

Simplify:

8K - 10 = 9K + 13

.

Rearrange:

8K - 9K = 13 + 10

→

-K = 23

→

K = -23

.

Answer:

K = -23

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