If 17 arithmetic means are inserted between 7 2 and - 83 2 , then the 17 t h arithmetic mean is

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Question: Answered & Verified by Expert

If

17

arithmetic means are inserted between

\frac{7}{2}

and

\frac{- 83}{2},

then the

17^{t h}

arithmetic mean is

MathematicsSequences and SeriesJEE Main

Options:

A $- 19$
B $- 29$
C $- 39$
D $- 49$

Solution:

1657 Upvotes Verified Answer

The correct answer is:

- 39

Let

d

be the common difference. Then

d = \frac{(- \frac{83}{2}) - (\frac{7}{2})}{18} = \frac{- 5}{2}

So, the

17^{t h}

mean is given by

- \frac{83}{2} - (- \frac{5}{2}) = - \frac{83}{2} + \frac{5}{2} = - \frac{78}{2} = - 39

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