Question

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

• A. $11$
• B. $19$
• C. $17$
• D. $18$

Answer 1

Answer: (D)

$18$

Answer 2

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, ${{T}_{5}}=a+4d$
$=-10+4(7)=-10+28$ $=18$