Question

Given the recursive or explicit formula find the first 3 terms

Answer 1

see explanation

Explanation:

(21)

using the recursive rule

a₁ = 6

a₂ = a₁ + 4 = 6 + 4 = 10

a₃ = a₂ + 4 = 10 + 4 = 14

first 3 terms are 6, 10, 14

(22)

using the recursive rule

a₁ = 26

a₂ = a₁ - 10 = 26 - 10 = 16

a₃ = a₂ - 10 = 16 - 10 = 6

first 3 terms are 26, 16 , 6

(23)

substitute n = 1, 2, 3 into the explicit formula

a₁ = - 3 ×
`3^((1-1))` = - 3 ×
`3^(0)` = - 3 × 1 = - 3

a₂ = - 3 ×
`3^((2-1))` = - 3 ×
`3^(1)` = - 3 × 3 = - 9

a₃ = - 3 ×
`3^((3-1))` = - 3 × 3² = - 3 × 9 = - 27

first 3 terms are - 3, - 9, - 27

(24)

substitute n = 1, 2, 3 into the explicit formula

a₁ = 2 ×
`(-5)^(1-1)` = 2 ×
`(-5)^(0)` = 2 × 1 = 2

a₂ = 2 ×
`(-5)^(2-1)` = 2 ×
`(-5)^(1)` = 2 × - 5 = - 10

a₃ = 2 ×
`(-5)^(3-1)` = 2 × (- 5)² = 2 × 25 = 50

first 3 terms are 2, - 10, 50