Question

determine wether each series is arithmetic or geometric. Then evaluate the finite series to the specified number of terms.
2+4+8+16+...;n=10

Answer 1

each term is the twice of the previous term - so what sequence?

Answer 2

i dont know

Answer 3

GP, is series where consecutive terms have a common ratio.

Answer 4

Arithmetic sequence is when you add the SAME number over and over. Another way to think about it is:


\(\Large \color{MidnightBlue}{\Rightarrow y_{2} - y_{1} = y_{3} - y_{2} }\)
Do you find any such pattern?

Answer 5

no, so its geometric

Answer 6

Yes. It is.

Answer 7

so how do i evaluate

Answer 8

\(\Large \color{MidnightBlue}{\Rightarrow {y_{2} \over y_{1}} = {y_{3} \over y_{2}} }\)

Answer 9

Do you know the formula to find the geometric series?

Answer 10

no

Answer 11

\(\Large \color{MidnightBlue}{\Rightarrow a{1 - r^{n} \over 1 - r} }\)

Here is the formula for you. 'n' is the nth term.

Answer 12

wait what is n?

Answer 13

what is a too?

Answer 14

n = 10...it's given

Answer 15

oh, what about r

Answer 16

r is the common ratio.

Answer 17

and A?

Answer 18

a is the first term in the geometric sequence.

Answer 19

2 in this case.

Answer 20

is the answer 198

Answer 21

Check it.

Answer 22

what is the arathmatic formula

Answer 23

The formula in the case would be:


\(\Large \color{MidnightBlue}{\Rightarrow 2({1 - 2^{10} \over 1 - 2}) }\)

Answer 24

no i need the arithmetic formula for this 2+4+6+8+...; n =128

Answer 25

Oh okay.

Answer 26

The formula for the sum of an arithmetic sequence is:


\(\Large \color{MidnightBlue}{\Rightarrow {n \over 2}(a_{1} + a_{last}) }\)

Answer 27

Thanks