Question

Given a series \( 5, 8, 11, 14, \dots \), if the \( n \)-th term of the given series is 320, then find \( n \) (where \( n \geq 1 \)):

• A. 104
• B. 105
• C. 106
• D. 107

Hint:

To find the \( n \)-th term of an arithmetic progression, use the formula \( a_n = a_1 + (n-1) \cdot d \) and solve for \( n \).

Answer 1

The Correct Option is C

Step 1: Identify the pattern of the series.
The given series is an arithmetic progression (A.P.), where the first term is \( a_1 = 5 \), and the common difference is: \[ d = 8 - 5 = 3. \] Step 2: Use the formula for the \( n \)-th term of an arithmetic progression: \[ a_n = a_1 + (n-1) \cdot d. \] Substitute the values \( a_n = 320 \), \( a_1 = 5 \), and \( d = 3 \) into the formula: \[ 320 = 5 + (n-1) \cdot 3. \] Step 3: Solve for \( n \).
First, subtract 5 from both sides: \[ 315 = (n-1) \cdot 3. \] Next, divide both sides by 3: \[ n-1 = 105. \] Finally, add 1 to both sides: \[ n = 106. \] Thus, the value of \( n \) is \( 106 \).