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
[tex]a_1=1st\text{ term};a_n=a_{n-1}+d[/tex]Where d is the common difference between each 2 consecutive terms
∵ The first term is 3
[tex]\therefore a_1=3[/tex]∵ The common difference is 2.5
∴ d = 2.5
→ Substitute them in the formula above
[tex]\therefore Q1_{}=3;Q_n=Q_{n-1}+2.5[/tex]∴ The recursive definition for the sequence is
[tex]Q_1=3;Q_n=Q_{n-1}+2.5[/tex]
