Question

The seventeenth term of the A. P. : 3, 8, 13, ... will be :

• A. 83
• B. 88
• C. 98
• D. 105

Hint:

The common difference $d$ is always $a_2 - a_1$. Always check if $a_3 - a_2$ gives the same result to confirm it is an A.P.

Answer 1

The Correct Option is A

To find the seventeenth term of the arithmetic progression (A.P.) given as 3, 8, 13, ..., we need to identify the initial term and the common difference of the sequence.

1. The first term \(a\) of the A.P. is 3.
2. The common difference \(d\) can be found by subtracting the first term from the second term. Thus, \(d = 8 - 3 = 5\).

We use the formula for the \(n\)th term of an A.P., which is:

\(T_n = a + (n - 1) \cdot d\)

Here, we need to find the 17th term, so \(n = 17\). Plugging the values of \(a\), \(d\), and \(n\) into the formula, we get:

\(T_{17} = 3 + (17 - 1) \cdot 5\)

Calculating inside the parenthesis first:

\(T_{17} = 3 + 16 \cdot 5\)

\(T_{17} = 3 + 80\)

\(T_{17} = 83\)

Therefore, the seventeenth term of the A.P. is 83.

1. To confirm, let's re-evaluate each step: Initial term \(a\) is confirmed as 3, and \(d\) correctly calculated as 5.
2. Substituting these into the A.P. formula verifies the calculation: \(T_{17} = 3 + 80 = 83\).

Thus, the correct option is 83.