Question

Write the explicit and exponential forms for the following:

1) a = 4 and r = 2
2) a = 12 and r = 6
3) a = 5 and r = 3
4) a = -7 and r = 2
5) a = 6 and r = 5
6) (2, 4, 8, 16,...)
7) (5, 15, 45, ...)

Answer 1

The explicit and exponential forms of the given sequences are provided with step-by-step explanations.

Step-by-step explanation:

1) Explicit form: a = 4, r = 2
an = a1 + (n-1)r
an = 4 + (n-1)2
an = 4 + 2n - 2
an = 2n + 2

Exponential form: a = 4, r = 2
an = arn-1
an = 4(2)n-1
an = 4(2n-1)

2) Explicit form: a = 12, r = 6
an = a1 + (n-1)r
an = 12 + (n-1)6
an = 12 + 6n - 6
an = 6n + 6

Exponential form: a = 12, r = 6
an = arn-1
an = 12(6)n-1
an = 12(6n-1)

3) Explicit form: a = 5, r = 3
an = a1 + (n-1)r
an = 5 + (n-1)3
an = 5 + 3n - 3
an = 3n + 2

Exponential form: a = 5, r = 3
an = arn-1
an = 5(3)n-1
an = 5(3n-1)

4) Explicit form: a = -7, r = 2
an = a1 + (n-1)r
an = -7 + (n-1)2
an = -7 + 2n - 2
an = 2n - 9

Exponential form: a = -7, r = 2
an = arn-1
an = -7(2)n-1
an = -7(2n-1)

5) Explicit form: a = 6, r = 5
an = a1 + (n-1)r
an = 6 + (n-1)5
an = 6 + 5n - 5
an = 5n + 1

Exponential form: a = 6, r = 5
an = arn-1
an = 6(5)n-1
an = 6(5n-1)

6) Explicit form: (2, 4, 8, 16, ...)
The explicit form of this sequence is:
an = 2n

Exponential form: (2, 4, 8, 16, ...)
The exponential form of this sequence is:
an = 2n

7) Explicit form: (5, 15, 45, ...)
The explicit form of this sequence is:
an = 5(3n-1)

Exponential form: (5, 15, 45, ...)
The exponential form of this sequence is:
an = 5(3n-1)