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
-22 - 11 = - 33
-33 / -3 = ?
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.
To find the number of terms in an arithmetic progression (AP), you can use the formula:
n = (last term - first term) / common difference + 1
Given that the first term (a) is 11, the last term (l) is -22, and the common difference (d) is -3, we can substitute these values into the formula:
n = (-22 - 11) / -3 + 1
Simplifying the expression, we have:
n = (-33) / -3 + 1
n = 11 + 1
n = 12
Therefore, there are 12 terms in the arithmetic progression.
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