Question

Find the$n^{th}$term of the AP if the$3^{rd}$term is 46 and$8^{th}$term is 131.

• A. (11n – 3)
• B. (11n – 7)
• C. (17n – 5)
• D. (13n – 5)
• E. (12n - 5)

Answer 1

The correct option is C (17n – 5)

Solution: Option (c)

$n^{th}$term of an A.P$\left(t_n\right)=a+(n-1)d$

$3^{rd}$term is$46,46=a+2d.........\left(i\right)$

$8^{th}$term is$131,131=a+7d..........\left(ii\right)$

Subtracting (i) from (ii) $5d=85\Rightarrow d=17anda=46-(2\times 17)=12$

$n^{th}$term$=a+(n-1)d=12+(n-1)17=17n-5$

Alternatively, substitute n=3 and n=8 in the answer options, to get 46 and 131. Only option (c) gives this value.