Question

Find the first five terms of the sequence: an = 5an – 1 + 2; a1 = 3.

a) {3, 17, 87, 437, 2187}

b) {3, 15, 75, 375, 1875}

c) {3, 12, 17, 22, 27}

d) {3, 11, 27, 59, 123}

Answer 1

Given that the series is given by:
an=5an-1+2
where:
a1=3
then the other terms of the sequence will be:
a2=5a1+2
a2=5*3+2=17

a3=5a2+2
a3=5(17)+2
a3=87

a4=5a3+2
a4=5(87)+2
a4=437

a5=5a4+2
a5=(5*437+2)
a5=2187

hence the sequence will be:
3, 17, 87, 437, 2187

Answer: a) {3, 17, 87, 437, 2187}