Question

The fifth term of an AP is 25 and the ninth term is 41. The first term of the AP is .

• A. 9
• B. 3
• C. 4

Answer 1

The correct option is A 9

Given that the fifth and the ninth terms of the AP are 25 and 41 respectively.
i.e., $a_5=25$ and $a_9=41$
If the common difference is taken as $d$, and the first term is taken as $a,$ then since the $n^{\text{th}}$ term of the AP is given by $a_n=a+(n-1)d,$ we have $a_5=a+(5-1)d=25$ and $a_9=a+(9-1)d=41.$
i.e., $a+4d=25$ ------------- (1)
$a+8d=41$ ------------- (2)
Subtracting equation (1) from equation (2), we get
$4d=16$
$\Rightarrow d=4.$
Substituting $d=4$ in equation (1)
$\Rightarrow a+(4\times 4)=25$
$\Rightarrow a=9$