Question

Write the first and fourth terms if the sequence whose nth term is given by the rule.

1. an=2n-1
2. an=12•3n
3. an=3n
4. an=5n+5
5. an=8-2n ​

Answer 1

Explanation:

1.

did you mean

an = 2n - 1

or did you mean

an = 2(n-1) ?

in the first case

a1 = 2×1 - 1 = 2 - 1 = 1

a4 = 2×4 - 1 = 8 - 1 = 7

in the second case

a1 = 2×(1 - 1) = 0

a4 = 2×(4 - 1) = 2×3 = 6

2.

a1 = 12×3×1 = 36

a4 = 12×3×4 = 144

3.

a1 = 3×1 = 3

a4 = 3×4 = 12

4.

did you mean

an = 5n + 5

or did you mean

an = 5(n + 5) ?

in the first case

a1 = 5×1 + 5 = 5 + 5 = 10

a4 = 5×4 + 5 = 20 + 5 = 25

in the second case

a1 = 5×(1 + 5) = 5×6 = 30

a4 = 5×(4 + 5) = 5×9 = 45

5.

did you mean

an = 8 - 2n

or did you mean

an = (8 - 2)n ?

in the first case

a1 = 8 - 2×1 = 8 - 2 = 6

a4 = 8 - 2×4 = 8 - 8 = 0

in the second case

a1 = (8 - 2)×1 = 6

a4 = (8 -2)×4 = 6×4 = 24

Answer 2

see explanation

Explanation:

substitute n = 1 and n = 4 into the nth term rules.

1

a₁ = 2(1) - 1 = 2 - 1 = 1

a₄ = 2(4) - 1 = 8 - 1 = 7

2

a₁ = 12 × 3(1) = 12 × 3 = 36

a₄ = 12 × 3(4) = 12 × 12 = 144

3

a₁ = 3(1) = 3

a₄ = 3(4) = 12

4

a₁ = 5(1) + 5 = 5 + 5 = 10

a₄ = 5(4) + 5 = 20 + 5 = 25

5

a₁ = 8 - 2(1) = 8 - 2 = 6

a₄ = 8 - 2(4) = 8 - 8 = 0