Question

the sum of the integers from 40 to 60, inclusive, is 1,050. what is the sum of the integers from 60 to 80, inclusive?

can you please sow me how to solve this problem

Answer 1

\[\sum_{k = a _{1}}^{a _{2}}k = \frac{ (a _{2} - a_{1} + 1)(a_{2} + a_{1}) }{ 2 }\]

Answer 2

Let me break it down for you:

\[\frac{ n(a_{1} + a_{2}) }{2 }\] is the typical way of writing this sum, with n being the number of terms being summed up, but I just went ahead and put in what it actually is, which is the upper bound minus the lower bound plus one (for inclusion).

Answer 3

So you would just plug in the numbers given to you, and you'll be able to find the summation.

Answer 4

what does a represent?

Answer 5

a1 is the smaller number and a2 is the larger number given to you. Basically the lower and upper bounds of the numbers you are trying to sum together. Does that make sense?

Answer 6

yes

Answer 7

Okay great, so then you just plug in the numbers you are given into a1 and a2 respectively and you'll find the summation.