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)

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, $T_5=a+4d$
$=-10+4(7)=-10+28$ $=18$