Question

what is the sum of the first 30 terms of an=3n+2

Answer 1

what is the first term, if \(n=1\) ?

Answer 2

there is no first term

Answer 3

?

Answer 4

what do you get if you replace \(n\) by \(1\) in \(a_n=3n+2\) ?

Answer 5

5 ?

Answer 6

right, so the first term is \(a_1=5\)
what is the last term, if \(n=30\) ?

Answer 7

92 ?

Answer 8

yes
what do you get when you add them?

Answer 9

i mean when you add \(a_1+a_{30}=5+92\) ?

Answer 10

97

Answer 11

yes
last step is to take half of 30, which is 15,and multiply \(15\times 97\)

Answer 12

so 1455 ?

Answer 13

and would you be able to help with something else ?

Answer 14

formula looks like
\[S=\frac{n}{2}\left(a_1+a_n\right)\] which in your case is
\[\frac{30}{2}(5+92)=15\times 97\]

Answer 15

sure i have one minute only though

Answer 16

if you save three pennies on january 1, six on january 2, 9 on january 3 and continue for 1 year not a leap year, what will be the value of your entire serving in dollars at the end of 1 year

Answer 17

even that was wrong, let me try again

Answer 18

\[3+2\times 3+3\times 3+...+364\times 3\]
\[a_1=3, a_n=3n\] first term is \(3\) last term is \(365\times 3\) add up
\[\frac{365}{2}(3+365\times 3)\]

Answer 19

so 133772.5 ?

Answer 20

now i got $2014.80