Question

Arithmetic sequence.
sequence 1: 2, 6,......
sequence 2: 24, 12,.....
sequence 3: 1, 5,......
Assuming that the sequences above are arithmetic with t(1) as the first term, find the next four terms for each sequence. For each sequence, write an explanation of what you did to get the next term and write an equation for t(n).

Answer 1

@jim_thompson5910 @dan815 @Nnesha

Answer 2

sequence 1:

first term is 2, second is 6

since 6-2 = 4, we are adding 4 to each term to get the next term

so the third term is 6+4 = 10
the fourth term is 10+4 = 14
etc etc

Answer 3

how would you put in an equation tho @jim_thompson5910

Answer 4

you use

t(n) = t(1) + d(n-1)

that's the general arithmetic formula

Answer 5

for sequence 1,

t(1) = 2 is the first term
d = 4 is the common difference

Answer 6

what do i put for n?

Answer 7

@jim_thompson5910

Answer 8

what do you get for t(n) ?

Answer 9

well what do i put for d(n-1), what do i put for this n? @jim_thompson5910

Answer 10

you leave n as it is

Answer 11

you'll get an expression in terms of n

Answer 12

you get t(n) = 4n-1

Answer 13

what is t(n) equal to when n = 1?

Answer 14

2?

Answer 15

t(n) = 4n-1

t(1) = 4(1)-1

t(1) = ??

Answer 16

t(1) + d(n-1)
2 + 4(1-1)
2 + 0 = 2 i thought you did this @jim_thompson5910

Answer 17

it works there, but it doesn't work with t(n) = 4n-1

Answer 18

oh ok

Answer 19

i get it thnx cx