Question

The sum of the first 30 terms of the sequence an = 6n + 5 is _____.

*** PLease explain cuz iheartfood is confused :(

Answer 1

Hi!!! THanks for coming to help again :)

Answer 2

the sum formular is
\[S _{n}=n/2(2a+(n-1)d)\]
n=number of terms
a=first term
d=common diff

Answer 3

so first we make the sequence

Answer 4

okay :) how do we make the sequence?

Answer 5

find 1st term 2nd term and so on.by plugging 1,2,3,4...

Answer 6

plug it into the sum formula??? that you wrote above?

Answer 7

or into 6n+5?

Answer 8

no we are jus looking for the terms,so in an=6n+5

Answer 9

oh okay... so like this?
6(1)+5=11
6(2)+5=17
etc..?

Answer 10

yes

Answer 11

so should i list them all out up to 30??

Answer 12

no the formular makes it easy well see later,
so whats
a=
d=
n=

Answer 13

oh okay! :) haha that would've taken a long time to write out :) so...
a=first term which is 11
d=common difference which is 6
n=number of terms which is 30
is that correct?

Answer 14

yes so look at the sum formular and substitute

Answer 15

S30=30/2(2(11)+(30-1)(6)) is that right so far?

Answer 16

and then i get 15(22+29(6))
which = 15(22+174)
which = 15(196)=2,940

Answer 17

so is the answer 2,940 ???? 2,940 is the sum of the first 30 terms of the sequence 6n+5???

Answer 18

yes so we dont have to write them until 30,exam questions can ask the sum of 300 terms

Answer 19

oh cool! so i just need to memorize these equations?

Answer 20

and so 2,940 is my final answer??

Answer 21

@Jonask the sum formula is the only formula i need to memorize to answer questions such as these yes??

Answer 22

but sometimnes there is a diff sum form

Answer 23

oh okay cool!! :) So 2940 is the final answer??? just making sure!! :)

Answer 24

\[S _{n}=n/2(a+l)\]

Answer 25

oh okay cool beans! :) Thanks @jonask :) u rock!! :)