Question

Determine 2nd term and rth term of a.p.whose 6 th term is 12 and 8 th term is 22​

Answer 1

Answer:   $\bold{a_2=-8\qquad \qquad a_r=5r-18}$

Step-by-step explanation:

Given: a₆ = 12     a₈ = 22

$d=\dfrac{a_8-a_6}{8-6}\quad = \dfrac{22-12}{8-6}\quad =\dfrac{10}{5}\quad =\boxed{5}$

$a_n=a_0+d(n-1)\\\\\\\underline{\text{Use}\ a_6\ \text{to find}\ a_o}\\a_6=a_o+5(6-1)\\\\12=a_o+5(6-1)\\\\12=a_o+25\\\\a_0=\boxed{-13}\\\\\\\underline{\text{Equation:}}\\a_n=13+5(n-1)\\.\quad =-13+5n-5\\.\quad =5n-18\\\\\\\underline{2^{nd\ term:}}\\a_2=5(2)-18\\.\quad = 10-18\\.\quad =\boxed{-8}\\\\\\\underline{r^{th}\ term:}\\\boxed{a_r=5r-18}$