Question

Find the sum 3 + 6 + 9 + ...... + 90

• A. 1395
• B. 1935
• C. 1359
• D. 1953

Answer 1

Answer:

A. 1395

The sum of the sequence is 1,395.

This is an Arithmetic Progression (AP) where numbers increase by a constant difference.

## 1. Identify the key components

* First term ($a$) = 3

* Common difference ($d$) = 6 - 3 = 3

* Last term ($l$) = 90

## 2. Find the total number of terms ($n$)

Use the formula for the $n$-th term: $l = a + (n-1)d$

$90 = 3 + (n - 1)3$

$90 - 3 = (n - 1)3$

$87 = (n - 1)3$

$n - 1 = \frac{87}{3} = 29$

$n = 29 + 1 = \mathbf{30}$

## 3. Calculate the sum ($S_n$)

Use the sum formula for an arithmetic series: $S_n = \frac{n}{2} (a + l)$

$S_{30} = \frac{30}{2} (3 + 90)$

$S_{30} = 15 \times 93$

$S_{30} = \mathbf{1395}$

## Final Answer

The sum of the series is 1,395.