Fill in blanks using Fibonacci sequence

Question

The Fibonacci sequence adds 2 previous numbers to get a third number. Eg: 1,1,2,3,5,8 etc. Use this info to obtain the sequence : 4,?,?,?,?,?, 62

Answer 1

4, a2, a3, a4, a5, a6, 62 Fibonacci sequence

62 = a5+a6 =2a5+ a4=2(a4+a3)+a4

= 3a4+2a3 =3(a3+a2)+2a3 = 5a3 +3a2

=5(a2+4)+3a2

= 8a2+20=62

a2 =(62-20)/8 =42/8 =5 1/4 = 5.25

a6 = a5+a4 = 23 3/4 +14 1/2 = 38 1/4

a5 = a4+a3 =14 1/2+9 1/4 = 23 3/4

a4 = a3+a2 = 9 1/4+5 1/4 = 14 1/2

a3 = a2+4 = 5 1/4 +4 = 9 1/4

4, 5 1/4, 9 1/4, 14 1/2, 23 3/4, 38 1/4, 62

missing terms are: 5.25, 9.25, 14.5, 23.75, 38.25