Question

use summation notation to write each arithmetic series for the specifies number of terms. Then evaluate the sum. 10+7+4+...; n=1

Answer 1

1 term, so the sum is just the 1st term: 10

Answer 2

Actually, we need to write the arithmetic series using summation notation first. The given series is:

10 + 7 + 4 + ...

The common difference between consecutive terms is -3 (subtracting 3 each time).

To write it using summation notation, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n-1)d

where a_n is the nth term, a_1 is the first term, d is the common difference, and n is the number of terms.

We know the first term a_1 = 10 and the common difference d = -3. We want to write the series for n = 1 term.

So, substituting these values in the formula, we get:

a_1 + (n-1)d = 10 + (1-1)(-3) = 10

Therefore, the series for n = 1 term is simply:

a_1 = 10

And the sum of this series is also 10.