Question

Determine the 2 and rth term of an ap whose6 term and 12 and 8 term idms 22

Answer 1

we know that ,nth term of AP
$an = a + (n - 1)d$
where a is first term and D is common difference.
Now 6 th term is
$12 = a + 5d$

8th term is 22
$22 = a + 7d$
from these two equation calculate a and d.
subtract both equation
$- 2d = - 10 \\ d = 5 \\ a + 5d = 12 \\ a + 25 = 12 \\ a = 12 - 25 \\ a = - 13$
first term is -13, common difference is 5.
2nd term is a+d=-13+5=-8
3rd term is a+2d= -13+10=-3