Question

Question #4Here are some values of sequence Q. Write a recursive definition for the sequence.n Q(n)1 33 87 18

Answer 1

n is the position of the term in the sequence

∵ At n = 1, Q(n) = 3

∵ At n = 3, Q(n) = 8

→ Let us divide the difference between and the first and third terms

by 2 to find the 2nd term

∵ 8 - 3 = 5 and 5/2 = 2.5

∴ At n = 2, Q(n) = 3 + 2.5 = 7.5

→ The recursive formula is

`a_1=1st\text{ term};a_n=a_(n-1)+d`

Where d is the common difference between each 2 consecutive terms

∵ The first term is 3

`\therefore a_1=3`

∵ The common difference is 2.5

∴ d = 2.5

→ Substitute them in the formula above

`\therefore Q1_{}=3;Q_n=Q_(n-1)+2.5`

∴ The recursive definition for the sequence is

`Q_1=3;Q_n=Q_(n-1)+2.5`