Question

Which expression represents the value of the series below?

3+7+11+ 15 + ... +1,671

1) 418
Σ [3+{n-1)4] n=1

2) 417
Σ [3+(n+1)4] n=1

3) 416
Σ [3+(n-1)4] n=1

4) 417
Σ[3+(n-1)4] n=1

Answer 1

A on 3dg

Explanation:

Answer 2

1) Σ [n=1, 418] (3+{n-1)4)

Explanation:

The expression for the sum is the sum over the number of terms of the expression for a general term.

__

general term

The general term of an arithmetic series is ...

an = a1 +d(n -1)

where a1 is the first term, and d is the common difference.

The given series has first term a1=3, and common difference d=7-3 = 4. Then the general term is ...

an = 3 +4(n -1)

number of terms

The last term will correspond to an n-value that can be found from ...

1671 = 3 +4(n -1)

1668 = 4(n -1) . . . . subtract 3

417 = n -1 . . . . . . . divide by 4

418 = n . . . . . . . add 1

sum expression

The expression for the sum is ...

`\displaystyle \boxed{\sum_(n=1)^(418)(3+(n-1)4)}`