Question

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

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

Answer 1

2(-2)^n-1

Explanation:

Correct on Odyssey assignment. Hope this helps.

Answer 2

`\bold{a_n=2\cdot(-2)^(n-1)}\\\\or\\\\\bold{a_n=(-1)^(n-1)\cdot2^(n)}`

Explanation:

-4÷2 = -2

8÷(-4) = -2

-16÷8 = -2

So this is a geometric sequence with the first term of 2 and a common ratio of -2

the nth term of a geometric sequence:
`a_n=a_1\cdot r^(n-1)`

Therefore:

`a_n=2\cdot(-2)^(n-1)\\\\a_n=2\cdot(-1\cdot2)^(n-1)=2\cdot(-1)^(n-1)\cdot2^(n-1)=(-1)^(n-1)\cdot2^(n-1+1)\\\\a_n=(-1)^(n-1)\cdot2^(n)`