Question

Write the first six terms of the sequence.

ao = -5, An = 3an-1 + 12

Answer 1

The first six terms of the sequence are -3, 3, 21, 74, 234 and 714

Explanation:

Given the initial value a0 = -5 and the general form of the sequence given as An = 3an-1 + 12

To get the first six terms of the sequence, we will substitute for n=1 up to n= 6 in the general equation.

when n=1

A1 = 3a(1-1)+12

A1 = 3a0+12

A1 = 3(-5)+12

A1 = -15+12

A1 = -3

when n=2;

`A2 = 3a(2-1)+12\\A2 = 3a1+12\\A2 = 3(-3)+12\\A2= -9+12\\A2= 3\\\\A3= 3a(3-1)+12\\A3= 3a2+12\\A3 = 3(3)+12\\A3= 9+12\\A3= 21\\\\A4= 3a(4-1)+12\\A4 = 3a3+12\\A4= 3(21)+12\\A4= 63+12\\A4 = 74\\\\A5= 3a(5-1)+12\\A5 = 3a4+12\\A5= 3(74)+12\\A5= 222+12\\A5 = 234\\\\\\A6= 3a(6-1)+12\\A6 = 3a5+12\\A6= 3(234)+12\\A6= 702+12\\A6 = 714\\`

The first six terms of the sequence are -3, 3, 21, 74, 234 and 714