Question

Identify the 10th term of the geometric sequence 7, –35, 175 ?
can someon show me how to do this please

Answer 1

ok - first you need to work out the common ratio between each term.
so, what do you need to multiply 7 by in order to get "-35"?

Answer 2

-5

Answer 3

correct. now as a quick check you can confirm that:

(-35) * (-5) = 175

Answer 4

yes

Answer 5

so now we know the common ratio and we also know the first term of the sequence commonly referred to as 'a' is equal to 7. in summary, we now know:

a=7
r=-5

Answer 6

okayy

Answer 7

next, you need to use the formulae for the n'th term of a geometric sequence. do you know the formula?

Answer 8

no i dont,

Answer 9

it might help you if you first refer to a quick refresher on geometric sequences. here is one: http://www.mathsisfun.com/algebra/sequences-sums-geometric.html

once you are ready, I can help you further if you still require help.

Answer 10

so do you just muliply each term by -5 ?

Answer 11

correct. the /long/ way of doing this would be to keep multiplying by -5 until you get to the 10'th term.
but you can use the formula for the n'th term and use that directly to get the 10'th term.

Answer 12

can you tell me the formula ? or is it the same formula for a arthmetic sequence
?

Answer 13

it is not the same as arithmetic sequences. the formula is given on that page if you scroll down a bit and look at the section titled "The Rule"

Answer 14

\[x_n=ar^{n-1}\]

Answer 15

Xn= ar ^(n-1) ?

Answer 16

yes - here 'a' is the first term
r is the common ratio
n is the index of the term you want - in this case 10

Answer 17

why 10 ?

Answer 18

because the question is asking you to find the 10'th term of the sequence

Answer 19

oh okay

Answer 20

so using the numbers we found, we get:\[x_{10}=7*(-5)^{10-1}=7*(-5)^9\]

Answer 21

and since 9 is an odd power, we know we must end up with a negative number. therefore:\[x_{10}=-7*5^9\]which you should be able to calculate using a calculator.

Answer 22

13,671,875 ?

Answer 23

remember the negative sign

Answer 24

-13,671,875 *

Answer 25

thats it - you got it! - well done!

Answer 26

so if the exponent is odd the answer will be negative ?

Answer 27

only if the common ratio is negative - which it was in this case (-5)

Answer 28

so if the common ratio is negative the answer is negative ?

Answer 29

if the common ration is negative, then the terms alternate between positive and negative values. you can see that from the first 3 terms given to you: 7, -35, 175

Answer 30

thanks you

Answer 31

yw