Question

Let t_n, n = 1,2,3,... be the n^th term of the A.P. 5, 8, 11,.... Then the value of n for which t_n = 305 is

• A. 101
• B. 100
• C. 103
• D. 99
• E. 95

Answer 1

The Correct Option is A

We are given the arithmetic progression (A.P.) with the first term \(t_1 = 5\) and the common difference \(d = 3\), and we are asked to find the value of \(n\) for which \(t_n = 305\).

The \(n\)-th term of an A.P. is given by the formula:

\(t_n = a_1 + (n-1) d\)

Substituting the given values \(a_1 = 5\) and \(d = 3\), we get: 

\(t_n = 5 + (n-1) \cdot 3\)

We are given that \(t_n = 305 , s\)

\(305 = 5 + (n-1) \cdot 3\)

Now, solve for \(n\):

\(305 - 5 = (n-1) \cdot 3\)

\(300 = (n-1) \cdot 3\)

\(n-1 = \frac{300}{3} = 100\)

\(n = 101\)

The value of \( n \) is 101.