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If $45, a, 2$ are in AP, then the value of a is

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\frac{4}{5}

\frac{7}{5}

\frac{3}{5}

\frac{1}{5}

answer is B.

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Detailed Solution

45, a, 2

are in AP, then the value of a is

75

.
It is given that

45, a, 2

are in AP.
From the given information,

a 1 = 45, a 2 = a, a 3 = 2

The consecutive terms have the same common difference. So,

a 2 − a 1 = a 3 − a 2

So, the common difference is given by,

a − 45 = 2 − a

5 a − 4 5 = 2 − a

5 a − 4 = 10 − 5 a

10 a = 14

a = 75

The value of a is

75

.
Hence option 2 is correct.

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