The first term of an AP is 5,the common difference is 3 and the last term is 80, find the number of terms

Question:

The first term of an arithmetic progression (AP) is 5, the common difference is 3, and the last term is 80. Find the number of terms.

Solution:

The formula for the nth term of an AP is:

an = a + (n - 1) * d

Given:

First term (a) = 5

Common difference (d) = 3

Last term (an) = 80

Substitute the values:

80 = 5 + (n - 1) * 3

80 - 5 = (n - 1) * 3

75 = (n - 1) * 3

75 / 3 = n - 1

25 = n - 1

n = 26

Answer:

The number of terms is 26.

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