The given series is 3, 6, 10, 15, 21, 28. We need to find the sum of the first ten terms of the series.


To find the sum of the first ten terms of the given series, we need to add up all the terms, i.e.,

Sum of first ten terms = 3 + 6 + 10 + 15 + 21 + 28 + ... (up to ten terms)

To find the pattern of the series, we can find the differences between the terms. The differences between the terms are:

6 - 3 = 3
10 - 6 = 4
15 - 10 = 5
21 - 15 = 6
28 - 21 = 7

We can see that the differences between the terms are increasing by 1. This means that the series is an arithmetic progression with a common difference of 1.

The formula for the sum of the first n terms of an arithmetic progression is:

S = n/2 * [2a + (n-1) * d]

where S is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

Using this formula, we can find the sum of the first ten terms of the given series as:

S = 10/2 * [2(3) + (10-1) * 1] = 55

Therefore, the sum of the first ten terms of the given series is 55.


The sum of the first ten terms of the given series 3, 6, 10, 15, 21, 28 is 55.