Question

PLEASE HELP!!!

Which Expression defines the arithmetic series 3 + 7 + 11 + . . . for eight terms?

Answer 1

Sure, let's take this step by step!

Firstly, we observe that the first term of the series is 3, and the common difference of the series (i.e., the difference between any two successive terms) is 4.

We wish to calculate the sum for the first eight terms.

Now, the formula for the last term (L) of an arithmetic progression series is L = a + (n-1)*d, where:
- a is the first term,
- n is the number of terms,
- d is the common difference.

So, to find the last term of our series we use the above formula, plugging in a=3, n=8, and d=4. We get:
L = 3 + (8-1)*4 = 3 + 7*4 = 31.

Now, the formula for the sum (S) of an arithmetic progression series is S_n = n/2 * (a + L), where:
- n is the number of terms,
- a is the first term,
- L is the last term.

Substitute the values n=8, a=3, and L=31 into the formula and we get:
S = 8/2 * (3 + 31) = 4 * 34 = 136.

Therefore, the expression which defines the arithmetic series 3 + 7 + 11 + .. for eight terms is: 8/2 * (3+31).

The sum of the series for the first eight terms is 136, and the last term of these eight is 31.

Answer 2

The first one is the best answer. Eight terms, common difference 4, first term 3, check.

Plenty of people (including me) write the second one as equivalent, but without the parentheses it's not clear if that final 1 is being summed or outside the summation so it's best fully parenthesized.