Question

Write the sum using summation notation, assuming the suggested pattern continues.

-4 + 5 + 14 + 23 + ... + 131

Answer 1

It seems to go by 9s.

Answer 2

it will help if you wrote down the partial sums

Answer 3

e.g.

sum to 1 term is -4
sum to 2 terms is -4 + 5 = -4 + (-4 + 9)
sum to 3 terms is -4 + 5 + 14 = -4 + (-4 + 9) + (-4 + 9 + 9)
etc

can you spot a pattern?

Answer 4

no i do not

Answer 5

try writing a few more partial sums and see if you can spot how this is growing

Answer 6

wait i do so the next one would be 32?

Answer 7

correct

Answer 8

and 32 can also be written as: -4 + 9 + 9 + 9 + 9

Answer 9

so each term in this sum can be written as -4 plus some multiple of 9

Answer 10

ok thank you so much

Answer 11

yw :)

Answer 12

can you help with a couple more things?

Answer 13

if you post each question in the list on the left then I am sure there are plenty of people on this site who will come to help you. I will try as well - but I also need to do some moderator duties, so I am not always fully available.

Answer 14

ok no problem