Question

If k-2,2k and 2k+7 are three consecutive terms of an AP,what is value of k?
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Answer 1

Given,

k -2, 2k & 2k+7 are consecutive terms of AP. Which means,

$2k - (k - 2) = 2k + 7 - 2k \\ \\ 2k - k + 2 = 7 \\ \\ k + 2 = 7 \\ \\ k = 7 - 2 \\ \\ k = 5$

Hope it helps.

Answer 2

If,

a, b and c are in AP thn,

we know,

b -a =  c - b = common difference

As per the question,

k-2 , 2k and 2k+ 7 are the three consecutive terms of an AP,

we can write,

$(2k)- (k-2) = (2k+7) - (2k) \\\\2k - k +2 = 2k + 7 - 2k\\\\k + 2 = 7 \\\\k = 5$

Thus the value of k is 5.