Question

Find the 8th term of the arithmetic sequence:
3, 8, 13, 18, ...
Find the 11th term of the arithmetic sequence:
-3, -5, -7, -9, ...

Answer 1

$a_1=3;\ a_2=8\\\\d=a_2-a_1\to d=8-3=5\\\\a_n=a_1+(n-1)d\to a_n=3+(n-1)\cdot5=3+5n-5=-2+5n\\\\a_8=-2+5\cdot8=-2+40=38\\----------------\\a_1=-3;\ a_2=-5\\\\d=a_2-a_1\to d=-5-(-3)=-5+3=-2\\\\a_n=a_1+(n-1)d\to a_n=-3+(n-1)(-2)\\=-3-2n+2=-1-2n\\\\a_{11}=-1-2\cdot11=-1-22=-23\\\\\\Answer:\boxed{a_8=38\ and\ a_{11}=-23}$