Question

what is the 50th term of the sequence that begins -4, 2, 8, 14?

Answer 1

this sequence seems to be an arithmetic sequence. then can you guess more about it?

Answer 2

basically you need to find the increment and then write the formula for the n-th term. (replace n wiht 50)

Answer 3

so whats the rule? +6?

Answer 4

i know theres probably some formula but i dont know what it is

Answer 5

The sequence begins with -4.
There is a common difference of +6 between each number.
To find any term in an arithmetic sequence use this.

\[a _{n} =a _{0} + (Deltax)(n-1)\]

Answer 6

\[a _{0} = 4; Deltax = 6; n = 50\]

Answer 7

i think your \(a_0\) should be \(a_1\), or \(n-1\) should be \(n\).

Answer 8

oops I mean -4

Answer 9

(a) 290
(b) 294
(c) 296
(d) 300

here are the answer choices. i'm trying to help my brother with his algebra but i dont remember how to do it and i dont understand the formula you gave

Answer 10

a

Answer 11

thank you:)

Answer 12

to go from one number of the sequence to the next number \(a_k\to a_{k+1}\), in an arithmetic sequence, you just add a certain constant number \(C\).
then it's again +C for the next one, +C for the next one , etc.
So you add n times the number C if you want to find a number that is at a distance n of the current number.

starting number: \(a_1=-4\).
number to find: \(a_{50}\).
number of steps: 49.
therefore, \(a_{50} = a_1 + 49 \times 6 = -4 + 294 = 290\), as DYHW said.

Answer 13

thank you that makes a lot of sense:) gotta love formulas lol

Answer 14

there are so many <3

Answer 15

why did you multiply 49 by 6?

Answer 16

oh nevermind figured it out

Answer 17

ok :D

Answer 18

so if i had this question "what is the 20th term of the sequence that begins -3, 6, -12, 24" it would be-3+49*___?

Answer 19

It is not an arithmetic sequence. (you don't add the same value at each step).
but there's another "constant operation". if you see what it is you can write , with the same method, the formula for a number at distance 'n' of some number.

Answer 20

do you see what happens at each step? seeing this will unlock everything..

Answer 21

well i know its multiplying by -2

Answer 22

that's it, then starting from a value \(x\) and making n steps will get you to the value \(x \times (-2)^n \).

Answer 23

so for n do i plug in 20? and im not sure what to plug in for x either

Answer 24

first term (\(a_1\)) of the sequence is a good choice for \(x\), n is the number of steps to get to \(a_{20}\).

Answer 25

so x= -3

Answer 26

yes, and the number of steps is 19 (not 20.. ). You'll need a computer to find the value of \(a_{20}\) but you can write the formula for it.

Answer 27

( we wrote everything already)
\(a_{20} = -3\times (-2)^{19}\).

Answer 28

explained*

Answer 29

awesome thank you:)) uve been a huge help!!

Answer 30

:D