Question

The first term of an arithmetic sequence is 6, the third is 17. Find the 30th.

Answer 1

do you know the equation for this?

Answer 2

yeah isnt it an=a+(n-1)d

Answer 3

here a=6 & a+2d=17,therefore u have 'd',nd then u hav 2 find a+29d..

Answer 4

where do we get the 2 from?

Answer 5

Adding on to what @campbell_st said:
Since our formula is: \[
a_n = a_1+(n-1)d
\]And we are given \( a_1=6,\;a_3=17\) we can make a system of equation(s): \[
a_3= 17 =6 + (3-1)d
\]Then you solve for \(d\)

Answer 6

then find a+29d for n=30..

Answer 7

would it be 6+2d?

Answer 8

cuz thats the 3rd term right?

Answer 9

i got 11/2

Answer 10

why is Tn? not really

Answer 11

oh so its the same thing as an?

Answer 12

okay so then i plug it in?

Answer 13

would it be an=6+11/2?

Answer 14

okay that helped a bit, so would it be an=15.31?

Answer 15

but what if i cant use the calculator

Answer 16

but what if i cant use any type of calculator tho/

Answer 17

to the n-1?

Answer 18

it was 30-1 and i got 29 which i timed it by 5.5 which i got 15.95

Answer 19

but i thought you said 5.5 . where did 5 and .05 come from?

Answer 20

yeah , where it says you multiply 29 times 5.5 5 and 0.5

Answer 21

?

Answer 22

29 *5.5 can't be 15.95. If you just drop the .5 from 5.5 and multiply by 29 you are going to get way more than 15.

Answer 23

okay, but why is it that you drop the 5 from 5.5?

Answer 24

To make your computation easier. We will multiply by .5 afterwards and add the result to what you get when you multiply 29 by 5.

Answer 25

29*5+29*0.5

Answer 26

is it cause it equals the same thing?

Answer 27

except one has a decimal and one doesn't/

Answer 28

when multiplying 29 and 5 you get what?

Answer 29

you get 145?

Answer 30

ok...good...now when you multiply 29 by 0.5 you get what?

Answer 31

14.5?

Answer 32

ok...so now add those two results together to get your final answer.

Answer 33

would it be 29?

Answer 34

How are you getting 29 when 29*5 is 145?

Answer 35

i mean 39

Answer 36

wait nevermind

Answer 37

Do you bnot remember the rule for adding two numbers with decimals?

Answer 38

not*

Answer 39

yes i do

Answer 40

would it be 159.5?

Answer 41

So, so far, you havee given one answer of 15.95, and now you have given me a 29 or a 39.

Answer 42

Finally!

Answer 43

There you go.

Answer 44

okay but can you explain to me why there are 5 and .5 tho?

Answer 45

Can't be too dependent on that calculator. Never know when you are going to be in a class where you can't use it.

Answer 46

Just another way to show that 29*5.5 =159.5 by splitting it up into 29*5 +29*.5