Question

The first and the last term of an AP are 11 and -22 respectively if the common different is -3 how many term are there

Answer 1

-22 - 11 = - 33

-33 / -3 = ?

Answer 2

when you have that quotient, add 1 to get the number of terms. The quotient tells you how many terms there are after the first one.

Answer 3

Use your definitions:
given: a = 11 and term(n) = a + (n-1)d = -22
but we know a = 11 and d = -3
11 + (n-1)(-3) = -22
-3n + 3 = -33
-3n = -36
n = 12 <------ you have 12 terms

check: term(12) = a + 11d = 11 + 11(-3) = -22