Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.
There is an example provided, (do not use the numbers in the example). Create your own!
let the first five terms of a sequence be 5, 10, 20, 40 and 80. these terms are taken from a geometric sequence with first term a15 and common ratio r=2 therefore we have a2=a1* r a3=a2 * r Therefore the recursive formula is an+1=2an, a1=5. and explicit formula is an=a1rn-1
Let the first five terms of a sequence be 3, 7, 16, 37, and 86.
To find the explicit formula, we can see that each term is increasing by adding the previous term and multiplying by a factor of 2. So, a1 = 3, r = 2.
The general term for the sequence can be written as: an = a1 * r^(n-1).
Thus, the explicit formula for the sequence is: an = 3 * 2^(n-1).
To find the recursive formula, we can see that each term is obtained by multiplying the previous term by 2 and then adding 1. So, an+1 = 2 * an + 1, with a1 = 3.
Therefore, the recursive formula for the sequence is: an+1 = 2 * an + 1.