Question

If a progression is given by 3,6,9,..... find the sum of the first eight terms

Answer 1

To find the sum of the first eight terms in a sequence, we need to use the formula for the sum of an arithmetic series.

First, let's find the common difference (d) in the given sequence. From the given sequence: 3, 6, 9, ..., we can see that the common difference (d) is 6 - 3 = 3.

Now, we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(2a + (n-1)d),

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

In this case, n = 8 (since we want to find the sum of the first eight terms), a = 3 (the first term), and d = 3 (the common difference).

Plugging in the values, we have:
Sn = (8/2)(2(3) + (8-1)(3))
= 4(6 + 7(3))
= 4(6 + 21)
= 4(27)
= 108.

Therefore, the sum of the first eight terms in the given sequence is 108.