Question

Which expression represents the value of the series below?

Answer 1

Answer:

  1) Σ [n=1, 418] (3+{n-1)4)

Step-by-step explanation:

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

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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 ...

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