Question

The sum of the first 10 terms of an AP with \(a=2\) and \(d=3\) is: 

• A. 155
• B. 145
• C. 165
• D. 150 Correct Answer: (A) 155 Solution:

Hint:

For AP problems involving sums, memorize: \[ S_n=\frac{n}{2}\left[2a+(n-1)d\right] \] It is one of the most frequently used formulas in sequences and series.

Answer 1

The Correct Option is A

Step 1: Write the sum formula.
The sum of the first $n$ terms of an AP is
\[ S_n = \frac{n}{2}\left[2a + (n-1)d\right] \]

Step 2: List the values.
Here $a = 2$, $d = 3$ and $n = 10$.

Step 3: Put them in.
\[ S_{10} = \frac{10}{2}\left[2(2) + 9(3)\right] = 5\left[4 + 27\right] = 5 \times 31 = 155 \]
\[ \boxed{155} \]