Find the number of terms in an ap given that it’s first and last terms are a and37a respectively and that it’ s common difference is4
In AP n-th term:
an = a + ( n - 1 ) d
where
a = first term
d = common difference
a1= a
an = 37a
d = 4 a
an = a + ( n - 1 ) d
37 a = a + ( n - 1 ) • 4 a
Subtract a to both sides.
36 a = ( n - 1 ) • 4 a
Divide both sides by 4a
9 = n - 1
Add 1 to both sides.
10 = n
n = 10
There are 10 terms in the AP