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If $k, 2 k - 1$ and $2 k + 1$ are three consecutive terms as an $A . P .$ , then find the value of $k$ .

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k = 2

k = 3

k = 4

k = 5

answer is B.

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Detailed Solution

Given that

k, 2 k - 1, 2 k + 1

are three terms in an A.P.
Let

a_{1} = k

a_{2} = 2 k - 1

a_{3} = 2 k + 1

We know

d = a_{n + 1} - a_{n}

Then, the common difference between first two terms,
d =

a_{2}

a_{1}

\Rightarrow

d =

2 k - 1 - k

\Rightarrow

d =

k - 1

Common difference between next two terms is,
d =

a_{3}

a_{2}

\Rightarrow d = 2 k + 1 - (2 k - 1)

\Rightarrow d = 2 k + 1 - 2 k + 1

\Rightarrow d

2

The common difference between the 2 consecutive terms should be equal.
Hence,

k - 1 = 2

\Rightarrow k = 2 + 1

\Rightarrow k = 3

Therefore, the value of

k = 3

.
Hence, option 2 is correct.

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