Find the number of terms in an AP given that it's first and last term are a and 37a respectively and that it's common difference is 4a

Answer 1

Let the number of terms in the arithmetic progression be n. The first term is a and the last term is 37a. The common difference is 4a.

We know that the nth term of an arithmetic progression is given by:
T_n = a + (n - 1)d

Substituting in the values, we have:
37a = a + (n - 1)(4a)

Simplifying the equation, we get:
37a = a + 4an - 4a

Combining like terms, we have:
37a = a(4n - 3)

Dividing both sides by (4n - 3), we get:
37a / (4n - 3) = a

Cancelling out the "a" terms, we have:
37 / (4n - 3) = 1

Simplifying the equation, we get:
37 = 4n - 3

Adding 3 to both sides, we have:
40 = 4n

Dividing both sides by 4, we get:
n = 10

Therefore, the number of terms in the arithmetic progression is 10.