Question

Find the 18^th and n^th term of the A.P. given by :
8, 13, 18,...

• A. 80,3+5n
• B. 93, 3+5n
• C. 65, 3-2n
• D. 40,5+3n

Answer 1

The Correct Option is B

The given sequence is an arithmetic progression (A.P.): 8, 13, 18,...

In an A.P., the general term (n^th term) is given by the formula:

a_n = a + (n - 1) * d

where "a" is the first term, "d" is the common difference, and "n" is the term number.

First, we calculate the common difference "d":

d = 13 - 8 = 5

The first term "a" is given as 8. Thus, the formula for the n^th term is:

a_n = 8 + (n - 1) * 5

By simplifying, we get:

a_n = 8 + 5n - 5 = 3 + 5n

To find the 18^th term, substitute n = 18 into the equation:

a₁₈ = 3 + 5 * 18

a₁₈ = 3 + 90 = 93

Therefore, the 18^th term is 93, and the n^th term is described by 3 + 5n. The answer is:

93, 3 + 5n