Question

The sum of the first 30 terms of the A.P. 1, 3, 5, 7, ... is:

• A. \( 900 \)
• B. \( 990 \)
• C. \( 890 \)
• D. \( 800 \)

Hint:

The sum of the first \( n \) terms of an A.P. is given by: \[ S_n = \frac{n}{2} (2a + (n-1)d). \]

Answer 1

The Correct Option is A

First term: \( a = 1 \), Common difference: \( d = 3 - 1 = 2 \), Number of terms: \( n = 30 \).
Using the sum formula for an A.P.:
\[ S_n = \frac{n}{2} (2a + (n-1) d) \] \[ S_{30} = \frac{30}{2} \times (2(1) + (30-1) (2)) \] \[ = 15 \times (2 + 58) \] \[ = 15 \times 60 = 900. \]