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match each verbal description of a sequence with its appropriate explicit function.
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a) aₙ = 4.(2)^n-1

b) aₙ = 2+3(n-1)

c) aₙ = 3+4(n-1)

d) aₙ = 3.(4)^n-1

Step-by-step explanation:

a) a geometric sequence with first term of 4 and a common ratio of 2

aₙ = ar^n-1

where a is the first term and r is the common ratio

aₙ = 4.(2)^n-1

Comparing with the standard form:

1st term = 4

Common ratio = 2

b) an arithmetic sequence with a first term of 2 and a common difference of 3

The standard form of arithmetic sequence is:

aₙ = a₁ + d(n-1)

where a₁ is the first term and d is the common difference

Given: aₙ = 2+3(n-1)

Comparing with standard equation

First term = 2

Common difference = 3

c) an arithmetic sequence with a first term of 3 and a common difference of 4

The standard form of arithmetic sequence is:

aₙ = a₁ + d(n-1)

where a₁ is the first term and d is the common difference

Given: aₙ = 3+4(n-1)

Comparing with standard equation

First term = 2

Common difference = 3

d) a geometric sequence with first term of 3 and a common ratio of 4

aₙ = ar^n-1

where a is the first term and r is the common ratio

aₙ = 3.(4)^n-1

Comparing with the standard form:

1st term = 3

Common ratio = 4