Write the first five terms of the sequence defined by the recursive formula an = 5an-1 -1, with a1=0

a9N0 = 5 a(n-1) - 1

a(1) = 0
a(2) = 5 a(1) - 1 = 5(0) - 1 = -1
a(3) = 5 a(2) - 1 = 5(-1) - 1 = -6
a(4) = .....

carry on

Oh, recursive formulas, how "formula-ble" you are. Let's get our funny gears spinning and calculate the first five terms of this sequence.

a1 = 0 (not very exciting, but hey, we have to start somewhere!)

a2 = 5a1 - 1 = 5(0) - 1 = -1 (ooh, negative numbers joining the party)

a3 = 5a2 - 1 = 5(-1) - 1 = -6 (the numbers seem to be sliding down)

a4 = 5a3 - 1 = 5(-6) - 1 = -31 (we're on a slippery slope here)

a5 = 5a4 - 1 = 5(-31) - 1 = -156 (this is sliding like penguins on ice)

So, the first five terms of the sequence are: 0, -1, -6, -31, -156. Now, that's just one way to describe a sequence, but I hope the humor made it a bit more enjoyable for you.

To find the first five terms of the sequence defined by the recursive formula an = 5an-1 -1, with a1=0, we can use the formula and calculate each term step by step.

Given: an = 5an-1 -1, with a1=0

To find a2:
a2 = 5a1 - 1
= 5(0) - 1
= -1

To find a3:
a3 = 5a2 - 1
= 5(-1) - 1
= -6

To find a4:
a4 = 5a3 - 1
= 5(-6) - 1
= -31

To find a5:
a5 = 5a4 - 1
= 5(-31) - 1
= -156 - 1
= -157

Therefore, the first five terms of the sequence are: 0, -1, -6, -31, -157.

To find the first five terms of the sequence defined by the recursive formula an = 5an-1 - 1, with a1 = 0, we will use a recursive approach.

Step 1: Start with the given value of a1 = 0.

Step 2: Use the recursive formula to find the next term, a2. Substitute the value of n = 2 into the formula:
a2 = 5a2 - 1
= 5 * a1 - 1
= 5 * 0 - 1
= -1.

Step 3: Repeat this process for the remaining terms:
To find a3, substitute n = 3 into the formula: a3 = 5a3 - 1 = 5 * a2 - 1 = 5 * (-1) - 1 = -6.

To find a4, substitute n = 4 into the formula: a4 = 5a4 - 1 = 5 * a3 - 1 = 5 * (-6) - 1 = -31.

To find a5, substitute n = 5 into the formula: a5 = 5a5 - 1 = 5 * a4 - 1 = 5 * (-31) - 1 = -156.

Step 4: Continue this process until you have found the desired number of terms. In this case, we need five terms.

Therefore, the first five terms of the sequence are:
a1 = 0,
a2 = -1,
a3 = -6,
a4 = -31,
a5 = -156.

The second -1 shouldnt be a subscript