Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each explicit formula to its corresponding recursive formula.
tiles:
f(n)=3+8(n-1)
f(n)=4+5(4)^n-1
f(n)=8+3(n-1)
f(n)=8+8(n-1)
f(n)=8(2)^(n-1)
f(n)=4+4(5)^n-1


pairs:
f(1)=8, f(n)=5f(n-1)-16 for n > 2 <------->
f(1)=8, f(n)=f(n-1)+8 for n > 2 <------->
f(1)=8, f(n)=3+f(n-1) for n>2 <------->

Please answer, I am so frustrated

Answer 1

Pair 1:

f(1)=8, f(n)=5f(n-1)-16 for n >2 and f(n)=4+4(5)^n-1

Pair 2:

f(1)=8, f(n)=f(n-1)+8 for n >2 and f(n)=8+8(n-1)

Pair 3:

(f)(1)=8, f(n)=3+f(n-1) for n>2 and f(n)=3+8(n-1)

Answer 2

Answer:

Pair 1:  f(1)=8, f(n)=5f(n-1)-16 for n > 2 <------->  f(n)=4+4(5)^n-1

Pair 2: f(1)=8, f(n)=f(n-1)+8 for n > 2 <------->  f(n)=8+8(n-1)

Pair 3:  f(1)=8, f(n)=3+f(n-1) for n>2 <-------> f(n)=8+3(n-1)

Step-by-step explanation:

In an explicit formula for a geometric sequence (a sequence in which each term is found by multiplying a constant to the previous term), the number that's multiplied each time (the common ratio) is raised to the n-1 power.

For the first pair, we see that we multiply 5 by the previous term each time; this means that in the explicit formula, 5 would be raised to the n-1 power.  We also see that f(1) = 8; this means the sequence starts at 8.  This means f(n)=4+4(5)^n-1 describes this sequence.

In an explicit formula for an arithmetic sequence (a sequence in which each term is found by adding a constant to the previous term), the number that's added each time (the common difference) is multiplied by n-1.

For the second pair, we see that we add 8 to the previous term each time; this means that in the explicit formula, 8 would be beside n-1.  We also see that f(1) = 8; this means the sequence starts at 8.  This means f(n)=8+8(n-1) describes this sequence.

For the third pair, we see that we add 3 to the previous term each time; this means that in the explicit formula, 3 would be beside n-1.  We also see that f(1) = 8; this means the sequence starts at 8.  This means f(n)=3+8(n-1) would describe this sequence.