Question

Write the nth term of the following sequence in terms of the first term of the sequence.

2, -4, 8, -16, . . .

Answer 1

ignore the alternating for the moent; is there a pattern you can pick up on?

Answer 2

Multiplying by 2

Answer 3

good, then we need to construct a recurrsion based on that knowledge i believe

Answer 4

\[A_{n+1}=2*A_n\]
but to include the alternating negative lets make it a -2\[A_{n+1}=-2*A_n\]

Answer 5

using this we can work it backwards to the A0 term

Answer 6

or we can go forwards with what is known .....

Answer 7

a1 = 2
a2 = a1*-2
a3 = a1*-2*-2 = a1 * (-2)^2
a4 = a1*(-2^2)*(-2) = a1*(-2)^3

if i assume a pattern

a5 = a1 * (-2)^4
a6 = a1 * (-2)^5

an = a1 * (-2)^(n-1)

Answer 8

Is the answer -(-2)^n?

Answer 9

"in terms of the first term of the sequence" whatever that my entail

but perhaps if we simplified it

Answer 10

how do you do it in terms of the first sequence?

Answer 11

replace a1 by its value of 2

im not sure if simplifying is what they want or not tho ....

Answer 12

do you know a trick to turn the sequence for all terms into a term for the first sequence?

Answer 13

What? what a1?

Answer 14

i do, there is a backwards version and a forwards version; i just showed you the forward version

Answer 15

a1 is the first term of the seq ..

Answer 16

an = a1 * (-2)^(n-1)
^^

Answer 17

I don't understand this at all. can you help me with a, a + 4, a + 8, . . .
That's 10 times the hell this question is

Answer 18

I don't even understand what the answer is

Answer 19

:"(

Answer 20

swearing at me doesnt make me want to help you much :/

Answer 21

i'm not swearing at you. Sorry, i'm very frustrated.

Answer 22

if we separate the terms

term : value
1: a
2: a+4
3: a+4+4
4: a+4+4+4
5: a+4+4+4+4

etc ....

Answer 23

I'll go relearn this instead. Thanks for your help.

Answer 24

we can then simplfy the results

term : value
1: a + 0(4)
2: a + 1(4)
3: a + 2(4)
4: a + 3(4)
5: a + 4(4)

notice that each term follows a pattern such that

n: a + (n-1)(4)

Answer 25

without knowing how the grading goes, thats prolly the best i can assess it