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  4. Four arithmetic means between -10 and 25 are inserted. Then the 5th term in the series is

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Q. Four arithmetic means between $-10$ and $25$ are inserted. Then the $5^{th}$ term in the series is

J & K CETJ & K CET 2010Sequences and Series

Solution:

Let $ {{A}_{1}},{{A}_{2}},{{A}_{3}} $ and $ {{A}_{4}} $ are inserted as arithmetic mean between
$ -10 $ and $ 25. $
Then, $ -10,\,{{A}_{1}},{{A}_{2}},{{A}_{3}},{{A}_{4}}\,\,25 $ are in AP.
Now, $ {{A}_{r}}=a+\frac{r(b-a)}{r+1} $
$ \therefore $ $ {{A}_{u}}=-10+\frac{4(35)}{5} $
$ =-10+28 $ $ =18 $
$ \therefore $ Fifth term is 18.
Alternate $ l={{T}_{n}}=a+(n-1)\,\,d $ $ 25=-10+(6-1)\,d $
$ 35=5d $
$ \Rightarrow $ $ d=7 $
Then, $ {{T}_{5}}=a+4d $
$ =-10+4(7)=-10+28 $ $ =18 $