Question

Which term of the A.P. 5, 8, 11, 14, ... is 38 ?

• A. 10th
• B. 11th
• C. 12th
• D. 13th

Hint:

You can also use a rearranged version of the formula to find 'n' directly: \(n = \frac{a_n - a}{d} + 1\). In this case, \(n = \frac{38 - 5}{3} + 1 = \frac{33}{3} + 1 = 11 + 1 = 12\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We need to find the position (\(n\)) of a specific term in a given Arithmetic Progression.

Step 2: Key Formula or Approach:
We will use the formula for the nth term of an A.P.:
\[ a_n = a + (n-1)d \] Here, we are given \(a_n\), \(a\), and we can find \(d\). We need to solve for \(n\).

Step 3: Detailed Explanation:
From the A.P. 5, 8, 11, 14, ...:
The first term, \(a = 5\).
The common difference, \(d = 8 - 5 = 3\).
The term we are looking for, \(a_n = 38\).
Substitute these values into the formula:
\[ 38 = 5 + (n-1)3 \] Now, solve for \(n\):
\[ 38 - 5 = (n-1)3 \] \[ 33 = (n-1)3 \] \[ \frac{33}{3} = n-1 \] \[ 11 = n - 1 \] \[ n = 11 + 1 = 12 \] So, 38 is the 12th term of the A.P.

Step 4: Final Answer:
38 is the 12th term.