If 17 arithmetic means are inserted between 7/2 and (-83)/2, then the 17^th arithmetic mean is

Correct answer: (C) -39. Let d be the common difference. Then d=(-83)/2-7/218=(-5)/2 So, the 17^th mean is given by -83/2--5/2=-83/2+5/2=-78/2=-39

Q45 / 118 · NTA Abhyas (JEE Main) 2020 · Mathematics · Sequences and Series

If $17$ arithmetic means are inserted between $\frac{7}{2}$ and $\frac{- 83}{2},$ then the $17^{t h}$ arithmetic mean is

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

Hence, the correct answer is option: 'C'.