Question

The first and last terms of an AP are 1 and 121 respectively. Find the number of terms in the AP if the common difference between them is:

A) 549
B) 671
C) 976
D) 1281

Answer 1

The number of terms in the arithmetic progression is 2 when the common difference is 549.

Step-by-step explanation:

The formula to find the number of terms in an arithmetic progression (AP) is:

n = (last term - first term) / common difference + 1

Given that the first term is 1, the last term is 121, and the common difference is A, we can substitute those values into the formula:

n = (121 - 1) / A + 1

Therefore, the number of terms in the AP with a common difference of A is (120/A) + 1.

So, to find the number of terms, divide 120 by each of the answer options and add 1:

A) (120/549) + 1 = 1.218 + 1 ≈ 2.218 ≈ 2

B) (120/671) + 1 = 0.179 + 1 ≈ 1.179 ≈ 1

C) (120/976) + 1 = 0.123 + 1 ≈ 1.123 ≈ 1

D) (120/1281) + 1 = 0.094 + 1 ≈ 1.094 ≈ 1

Therefore, the correct answer is A) 549, which results in 2 terms in the arithmetic progression.