Write the first five terms of the sequence defined by the recursive formula an=2(an-1)+3 with a1=-2
Oh, recursive sequences! They always make me want to curl up into a ball and ponder the mysteries of life. But fear not, dear human! I'm here to help. Let's find the first five terms of this sequence.
Using the given recursive formula, we have:
a1 = -2 (they gave that to us)
a2 = 2(a1) + 3 = 2(-2) + 3 = -4 + 3 = -1
a3 = 2(a2) + 3 = 2(-1) + 3 = -2 + 3 = 1
a4 = 2(a3) + 3 = 2(1) + 3 = 2 + 3 = 5
a5 = 2(a4) + 3 = 2(5) + 3 = 10 + 3 = 13
Thus, the first five terms of this sequence are: -2, -1, 1, 5, 13. Voila!
To find the first five terms of the sequence defined by the recursive formula an=2(an-1)+3 with a1=-2, we can plug in the values of n starting from 1 and calculate each term.
a1 = -2 (given)
Using the recursive formula:
a2 = 2(a1) + 3 = 2(-2) + 3 = -4 + 3 = -1
a3 = 2(a2) + 3 = 2(-1) + 3 = -2 + 3 = 1
a4 = 2(a3) + 3 = 2(1) + 3 = 2 + 3 = 5
a5 = 2(a4) + 3 = 2(5) + 3 = 10 + 3 = 13
Therefore, the first five terms of the sequence are: -2, -1, 1, 5, 13.
To generate the first five terms of the sequence defined by the recursive formula an = 2(an-1) + 3 with a1 = -2, we can follow these steps:
1. Start with the initial term a1.
- In this case, a1 = -2.
2. Use the recursive formula to find the next term, a2.
- Plug in the value of a1 into the formula:
a2 = 2(a1) + 3
= 2(-2) + 3
= -4 + 3
= -1
3. Repeat step 2 to find a3, a4, and a5.
- For a3:
a3 = 2(a2) + 3
= 2(-1) + 3
= -2 + 3
= 1
- For a4:
a4 = 2(a3) + 3
= 2(1) + 3
= 2 + 3
= 5
- For a5:
a5 = 2(a4) + 3
= 2(5) + 3
= 10 + 3
= 13
Therefore, the first five terms of the sequence are:
a1 = -2, a2 = -1, a3 = 1, a4 = 5, a5 = 13.
also simple
a1 = -2
a2 = 2(a1)+3 = 2(-2)+3 = -1
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