The partial sum 1 + 5 + 9 + ⋯ + 77 equals (Help pls)

Question

The partial sum 1 + 5 + 9 + ⋯ + 77 equals: ______

Answer 1

find the sum of 1+5+9+...+77

77/4=19 1/4 so there are 20 numbers

use the arithmetic sequence sum formula

S_n=n(a₁+a_n)/2 where n=20, a₁=1 (first term) and a_n=77 (last term)

S_n=20(1+77)/2

S_n=10(78)

S_n=780

you don't want to add them all together because you might have 100 numbers for example

also, realize that 1+77=78, 5+73=78, 9+69=78 and so on

you have 10 sums of 78 so 10*78=780

in case you forget the formula !

Answer 2

Hi Alexus,

Your group of numbers is the sum of all numbers (1+ 4i) starting with i=0 to i=19.

So it means you have 20 numbers you need to sum up. 1+5+9+13+....

You stat with the number 1 and add 4, then you add 4 to that number and so on. That is how you get the numbers of the sequence.

If you add up all numbers from 1 to 77 your sum will be 780

I made some assumptions on your knowledge of sequences. If you need a more detailed explanation feel free to contact me.