What’s the first four terms of a1=-2, An=-3an-1+7. For. N>2
To find the first four terms of the given sequence, we'll use the recursive formula provided.
a₁ = -2
aₙ = -3aₙ₋₁ + 7, for n > 2
To find a₂, we substitute n = 2 into the formula:
a₂ = -3a₁ + 7 = -3(-2) + 7 = 6 + 7 = 13
Now, to find a₃, we substitute n = 3:
a₃ = -3a₂ + 7 = -3(13) + 7 = -39 + 7 = -32
Lastly, to find a₄, we substitute n = 4:
a₄ = -3a₃ + 7 = -3(-32) + 7 = 96 + 7 = 103
Therefore, the first four terms of the sequence are:
a₁ = -2
a₂ = 13
a₃ = -32
a₄ = 103
To find the first four terms of the sequence defined by the given recursive formula, you need to apply the formula repeatedly.
The formula states that An equals -3 times the previous term (An-1) plus 7. We are given that A1 is equal to -2, which will serve as the starting point.
1. First, we substitute n = 1 into the formula to find A2.
A2 = -3A1 + 7
A2 = -3(-2) + 7
A2 = 6 + 7
A2 = 13
2. Next, we substitute n = 2 into the formula to find A3.
A3 = -3A2 + 7
A3 = -3(13) + 7
A3 = -39 + 7
A3 = -32
3. Then, we substitute n = 3 into the formula to find A4.
A4 = -3A3 + 7
A4 = -3(-32) + 7
A4 = 96 + 7
A4 = 103
Therefore, the first four terms of the sequence are:
A1 = -2
A2 = 13
A3 = -32
A4 = 103
just plug in the various values of n.
a1 = -2
a2 = -3a1 + 7 = -3(-2)+7 = 13
now go on from there