Question

Which recursive definition produces an arithmetic sequence where g(5) = 8 and g(10) = 10? Select one: 1) g(n) = g(n − 1) + 0.4 where g(1) = 6 2) g(n) = 1.069(n − 1) where g(1) = 6.4 3) g(n) = 1.069(n − 1) where g(1) 4) g(n) = g(n-1) + 0.4 where g(1) = 6.4

Answer 1

To determine which is the arithmetic sequence, it is necessaryto replace the values of n in the given function until finding the required results (g(5) = 8 and g(10) = 10), just as follow:

1)

g(n) = g(n-1) + 0.4

g(1) = 6

g(5) = g(4) +0.4 = g(3) +0.4 +0.4 = g(2) +0.4 +0.4 +0.4

= g(1) + 0.4 +0.4 +0.4 +0.4 = 6 + 1.6 = 7.6

Then, this is not the sequence.

2)

g(n) = 1.06*g(n - 1)

g(1) = 6.4

g(5) = 1.06*g(4) = 1.06*1.06g(3) = 1.06*1.06*1.06*g(2)

= 1.06*1.06*1.06*1.06*g(1) = 1.06*1.06*1.06*1.06*6.4 = 8.07

Then, this is not the sequence

4)

g(n) = g(n - 1) + 0.4

g(5) = 6.4 + 0.4 +0.4 +0.4 +0.4 = 8

g(10) = g(9) + 0.4 = g(8) +0.4 +0.4 = g(7) +0.4 +0.4 +0.4

= g(6) + 0.4 +0.4 +0.4 +0.4 = g(5) +0.4 +0.4 +0.4 +0.4 +0.4

= 8 + 2 = 10

The last results give the required results. Hence, g(n) = g(n - 1) + 0.4 is the searched recursive arithmetic sequence.