Question

Find the nth term of the following sequences. Also find the 9th and 6th terms .​

Answer 1

Answer: an=2(-2)ⁿ⁻¹ a₉=512 a₆=-64

Explanation:

Since we have an alternating minus sign in this sequence, therefore the first multiplier of the following sequence will be (-1)ⁿ.

And since the first term of the following sequence is positive, the first multiplier of the following sequence is (-1)ⁿ⁻¹.

The second multiplier of the following sequence is 2ⁿ because the sequence has the form: 2, 4, 8, 16, ..., 2ⁿ .

`Thus,\ a_n=(-1)^(n-1)(2^n)\\\\ a_n=2(-2)^(n-1)\ \ \ (1)`

Find the 9th and 6th terms of the sequence by formula (1):

a₉=2(-2)⁹⁻¹

а₉=2(-2)⁸

a₉=2(256)

a₉=512

a₆=2(-2)⁶⁻¹

а₆=2(-2)⁵

a₆=2(-32)

a₆=-64