Question

for what value of k will K + 9, 2K -1 and took k + 7 are the consecutives terms of an ap

Answer 1

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Let,

$\mathsf{a_1}$ = K + 9

$\mathsf{a_2}$ = 2K - 1

$\mathsf{a_3}$ = K + 7

If these 3 terms are in A.P. ( Arithmetic Progession ), then the common Difference will be same.

•°•

$\mathsf{a_2}$ - $\mathsf{a_1}$ = $\mathsf{a_3}$ - $\mathsf{a_2}$

( 2K - 1 ) - ( K + 9 ) = ( K + 7 ) - ( 2K - 1 )

2K - 1 - K - 9 = K + 7 - 2K + 1

K - 10 = - K + 8

K + K = 8 + 10

2K = 18

K = 18 / 2

K = 9

Hence,

Value of K is 9.

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Answer 2

Answer:

k = 9

Step-by-step explanation:

AP: K + 9, 2K -1, k + 7

Find the Common difference between a1 and a2:

a2 - a1 = (2k - 1) - (k + 9)

a2 - a1 = 2k - 1 - k - 9

a2 - a1 = k - 10

Find the common difference between a2 and a3:

a3 - a2 = (k + 7) - (2k - 1)

a3 - a2 = k + 7 - 2k + 1

a3 - a2 = 8 - k

Solve k:

k - 10 = 8 - k

2k = 18

k = 9

Answer: k = 9