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

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

Sagot :

Unicorn3125idn

Answer:

        [tex]\bold{a_n=2\cdot(-2)^{n-1}}\\\\or\\\\\bold{a_n=(-1)^{n-1}\cdot2^{n}}[/tex]

Step-by-step 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:  [tex]a_n=a_1\cdot r^{n-1}[/tex]

Therefore:

            [tex]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}[/tex]

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