Question

find the sum
3+10+17+24+...+7003+7010

Answer 1

i did this ,but im sure im missing something

7010-3/2

Answer 2

yeah, somethings off with that

Answer 3

what type of pattern do we have?

Answer 4

arithmetic sequence

Answer 5

good, then we should be able to add the first and last as part of the process. knowing how many terns there are tho is also needed

Answer 6

\[\frac{n}{2}(first+last)\]

Answer 7

so then it would be (7010)/2(3+7010) like this

Answer 8

there are not 7010 terms, but you are on the right track

Answer 9

what is our common difference? what is added to get a new term?

Answer 10

there is a finite number which stops at 7010 so should i apply the formula an=a1+(n-1)d

Answer 11

you should yes

Answer 12

but i don't know the common difference
it goes 3 to 7 to 7 again
it's not constant

Answer 13

3+10+17+24+...+7003+7010
7 7 7 7

Answer 14

ohhh oops
lol

Answer 15

i didn't follow clearly no wonder

Answer 16

on a small scale, lets say our difference is 4:

2,6,10,14 we have 4 terms

we can adjust it by subtracting 2 from it all

0,4,8,12, now divide by 4

0,1,2,3 ... the number of terms is 1 more than the last adjusted term

Answer 17

n = (7010-3)/7 + 1

Answer 18

i spose we could have done the same with the rule:

an = ao + (n-1)d

an - ao = (n-1)d

(an - ao)/d = n-1

(an - ao)/d + 1 = n

Answer 19

an=3+(7010-1)7

Answer 20

n-1, not 7010-1 you are trying to find the value of n

Answer 21

the an term? would be 7010 is that right

Answer 22

ohh ok

Answer 23

7010 = 3 + 7(n-1)

yes, solve for n

Answer 24

makes sense now thanks for the clarification

Answer 25

good luck ;)