Answer:
2a. aₙ = 12 * -2ⁿ⁻¹; a₈ = -1536
2b. aₙ = 4 * 3ⁿ⁻¹; a₈ = 8748
Step-by-step explanation:
The geometric sequence formula is aₙ = a₁ * rⁿ⁻¹.
2a:
a₈ = 12 * -2⁸⁻¹ <em>{Subtract 1 from 8 to get 7}</em>
a₈ = 12 * -2⁷ <em>{2⁷ is 128. Since the exponent is odd, this will be negative.}</em>
a₈ = 12 * (-128) <em>{Multiply 12 by -128 to get -1536.</em>
a₈ = -1536
2b:
a₈ = 4 * 3⁸⁻¹ <em>{Subtract 1 from 8 to get 7)</em>
a₈ = 4 * 3⁷ <em>{7 is the 3rd number after 4 (a multiple of 4). As a result, this will end in a 7. 3⁷ is 218</em><em>7</em><em>.}</em>
a₈ = 4 * 2187 <em>{Multiply 4 by 2187 to get 8748}</em>
a₈ = 8748