Question

Suppose that a sequence is defined as follows.a₁ = -4, an=3an-1+7 for n>2List the first four terms of the sequence.

Answer 1

The sequence is defined as

an = 3an - 1 + 7

This means that

a2 = 3(a(2 - 1) + 7

a2 = 3a1 + 7

From the information given ,

a1 = - 4

Thus,

a2 = 3 * - 4 + 7 = - 12 + 7

a2 = - 5

a3 = 3(a(3 - 1) + 7

a3 = 3a2 + 7

a3 = 3 * - 5 + 7 = - 15 + 7

a3 = - 8

a4 = 3(a(4 - 1) + 7

a4 = 3a3 + 7

a4 = 3 * - 8 + 7 = - 24 + 7

a4 = - 17

Thus, the first four terms of the sequence are

- 4, - 5, -