Question

Find the sum of the arithmetic series.

1 + 4 + 7 + 10 + ... + 43

Answer 1

@ganeshie8

Answer 2

how??? ;-;

Answer 3

okay well a_1=1

Answer 4

yes

Answer 5

how much is it increasing each time?

Answer 6

3

Answer 7

correct so d is 3

Answer 8

I am not sure, but does this work to present this situation?
\[\sum_{n=1}^{43}n + 3\]

Answer 9

to get the sum this is your formula \[s_n=\frac{ n }{ 2 }[a_1+a_n]\]

Answer 10

yes

Answer 11

plug in a_1=1 and a_n=43 and n=?

Answer 12

but first we need to find n

Answer 13

which n=14

Answer 14

how did you get 14?

Answer 15

kept adding 3 in my head till i got 43

Answer 16

ok. is there any algebraic way to find n?

Answer 17

i mean i know that if we know what \(S_n\) then it can be possible, but in this case would it work?

Answer 18

yes lemme get it for you

Answer 19

ok

Answer 20

1+(n-1)*3=43

n=15 not 14 sorry

Answer 21

okay so you use the explicit formula to find this right?

Answer 22

a_1+(n-1)*d=a_n yes this is explicit

Answer 23

thanks! can you help me with one more problem?

Answer 24

I can sure try to! Tag me in your new thread.