Question

In an AP, the first term is 7 and the common difference is 4. Which term of the AP will be five times the first term?

• A. $8^{th}$ term
• B. $4^{th}$ term
• C. $2^{nd}$ term
• D. ${12}^{th}$ term

Answer 1

The correct option is A

$8^{th}$ term

Formula to find $n^{th}$ term of arithmetic progression is

$t_n=a+(n-1)d$

where,

'$a$' is the first term,

'd' is the common difference,

'n' is the no. of terms,

'$t_n$' is the $n^{th}$ term.

Given,

first term, a = 7 and common difference, d = 4
$a_n=$ $5a$
$5a=5\times 7=35$
Now, $n^{th}$ term of the AP, $t_n=a+(n-1)d$
$t_n=7+(n-1)4$
$35=7+(n-1)4$
$n-1=7$
$n=8$
$\therefore$ $8^{th}$ term of the AP is five times the first term.