Question

The first term of an arithmetic progression (AP) is 5, the last term is 45, and the sum of all its terms is 400. Find the number of terms.

a. 10
b. 15
c. 20
d. 25

Answer 1

The number of terms in the given arithmetic progression is 16.

To find the number of terms in an arithmetic progression (AP) with a given first term, last term, and sum of terms, we can use the formula:

Sum of terms = (number of terms / 2) * (first term + last term)

Plugging in the given values, we have:

400 = (number of terms / 2) * (5 + 45)

Simplifying the equation, we get:

400 = (number of terms / 2) * 50

Dividing both sides by 50, we get:

8 = number of terms / 2

Multiplying both sides by 2, we get:

16 = number of terms

Therefore, the number of terms is 16.