Question

For the sequence, describe the pattern, write the next term, and write a rule for the nth term

2,4,8,16

Answer 1

did you notice any pattern ?

Answer 2

x2

Answer 3

\(x^2\)
are you sure ?
or you mean
\(2^x\)
?

Answer 4

i mean it times 2

Answer 5

ohh, then you're correct.

Answer 6

so what term comes after 16 ?

Answer 7

32

Answer 8

help me please hartnn from bigpapa021201

Answer 9

yes.
so, for n=1, you have 2 = 2^1
for n=2, you have 4 = 2^2
and so on....
can you find the n'th term rule now ?

Answer 10

wait so do i write the nth term rule for 32?

Answer 11

help me ammarahplease from bigpapa021201

Answer 12

so one help me

Answer 13

n'th term rule is for entire sequence

Answer 14

so i would do it for each one?

Answer 15

finding n'th term is just once, per sequence, and that n'th term rule applies to all terms,...
let me give you example

3,6,9,12....
so, the rule is n times 3,
so, f(n) here will be 3n


what about 2,4,8,16,32...
try ?

Answer 16

2n

Answer 17

not actually, the 2n sequence is

2,4,6,8,10,12....is that your sequence ?

Answer 18

note that the terms increase exponentially

Answer 19

2^n

Answer 20

thats absolutely correct! :)

Answer 21

how about 3,5,7,9 would this be 2+n

Answer 22

2nd term , put n= 2 in 2+n
so, is the 2nd term = 2+2 = 4 ??

try again ...

Answer 23

you're close though....
think of the sequence,
2,4,6,8,10.....and that you add 1 to each term of these

Answer 24

? idk

Answer 25

learnt about arithmetic sequence and common difference yet ?

Answer 26

yes

Answer 27

whats the common difference of this sequence ?

Answer 28

\(a_n = a+ (n-1)d\)
here a= first term = 3
d= ...?

Answer 29

2

Answer 30

yes,

so the rule here will be
an = 3+ (n-1)*2

simplify this!

Answer 31

how about this one: 1/1,1/4,1/9,1/16

Answer 32

you need n'th term ??

look at denominators...

1,4,9,16...
notice any pattern ?

Answer 33

is the same yes write a rule for the nth term

Answer 34

i dont see a pattern

Answer 35

hint : squares of integers

Answer 36

2^n

Answer 37

so how would i write that

Answer 38

not actually, the denominator pattern is
n^2

n= 1, >>>>1
n=2 >>>>>2^2 = 4
n=3 >>>>>3^2 =9
...
got this ?

Answer 39

yes

Answer 40

and the numerator is always 1
so, your n'th term rule is simply
1/n^2
thats it!

Answer 41

how would i write the series using summation notation

2/3+4/5+6/6+8/7

Answer 42

numerator sequence = 2,4,6,8....

i don't see any pattern in denominator....is the question correct ?

Answer 43

yeah..

Answer 44

I have to go to sleep...tell me if u figure out the prob please

Answer 45

ok,
and good night!
sweet dreams :)