Consider a sequence of numbers given by the expression 7 + (n - 1) * 5

We are given the sequence 7 + (n - 1) * 5, in which n spans from 1 to 80. Let’s determine the first few values of the sequence.

n = 1

7 + (0 x 5) = 7

n = 2

7 + (1 x 5) = 12

n = 3

7 + (2 x 5) = 17

n = 4

7 + (3 x 5 ) = 22

We see that we have an evenly spaced set in which each term is 5 apart. To determine the sum, we can use the formula: sum = average x quantity. Since we know the quantity is 80, we need to determine the average.

We can use the formula: average = (first term in the set + last term in the set)/2

The last term in the set is 7 + (79 x 5) = 402, and thus:

average = (7 + 402)/2 = 409/2

Now we can calculate the sum:

sum = (409/2) x 80 = 16,360

Answer: C

Kudos for the formula- I wanted to ask you- I see similar series problems on Veritasprep and wanted to ask if this formula is universal (I think it is). I have never seen this formula but now it makes a lot of sense- where did you get this formula from?

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