Q:

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-1f(n)=8+3(n-1)f(n)=8+8(n-1)f(n)=8(2)^(n-1)f(n)=4+4(5)^n-1pairs: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

Accepted Solution

A:
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.