Question

Find the $8^{th}$ term of an A.P whose ${15}^{th}$ term is $49$ and ${19}^{th}$ term is $65$

Answer 1

$t_{15}=a+14d=49$

$t_{19}=a+18d=65$

Subtract $a+18d-a-14d=65-49$

$\Rightarrow 4d=16$

$\therefore d=\frac{16}{4}=4$

From $\left(1\right)\Rightarrow a+14\times 4=49$ where $d=4$

$\Rightarrow a=49-56=-7$

$t_8=a+(8-1)d$

$t_8=-7+7d=-7+28=21$