Question

The sum of the first 24 terms of the series 9+13+17+...... is equal to

• A. 1212
• B. 1200
• C. 1440
• D. 1320
• E. 1230

Answer 1

The Correct Option is D

We are given an arithmetic series:

\[ 9 + 13 + 17 + \dots \] This is an arithmetic progression (AP) where:

• First term \( a = 9 \)
• Common difference \( d = 13 - 9 = 4 \)

We need to find the sum of the first 24 terms of this series. The formula for the sum of the first \( n \) terms of an arithmetic progression is:

\[ S_n = \frac{n}{2} \left( 2a + (n - 1) d \right) \] Substituting the values \( a = 9 \), \( d = 4 \), and \( n = 24 \) into the formula, we get: \[ S_{24} = \frac{24}{2} \left( 2(9) + (24 - 1) \times 4 \right) \] \[ S_{24} = 12 \left( 18 + 23 \times 4 \right) \] \[ S_{24} = 12 \left( 18 + 92 \right) \] \[ S_{24} = 12 \times 110 = 1320 \]

Thus, the sum of the first 24 terms is \(1320\).

The correct option is (D) : \(1320\)

Answer 2

The given series is an arithmetic progression (A.P.) with the first term \(a = 9\) and the common difference \(d = 13 - 9 = 4\).

The formula for the sum of the first \(n\) terms of an A.P. is:

\[ S_n = \frac{n}{2} \left(2a + (n - 1) \cdot d\right) \]

We are asked to find the sum of the first 24 terms, so \(n = 24\), \(a = 9\), and \(d = 4\). Substituting these values into the formula:

\[ S_{24} = \frac{24}{2} \left(2 \cdot 9 + (24 - 1) \cdot 4\right) \] \[ S_{24} = 12 \left(18 + 23 \cdot 4\right) \] \[ S_{24} = 12 \left(18 + 92\right) \] \[ S_{24} = 12 \times 110 = 1320 \]

Therefore, the sum of the first 24 terms of the series is 1320.