Find the first 4 terms of the recursively defined sequence.
a subscript 1 =9, a subscript 2 =9, a Subscript n+1=a Subscript n +a Subscript n-1
Are the first four terms
A)9,9,18,18
B)9,9,9,27
C)9,9,81,729
D)9,9,18,27
what's the trouble? Each term, starting with the 3rd, is the sum of the two previous terms.
Since the first two terms are 9,9 the sequence continues with
9+9 = 18
9+18 = 27
18+27 = 45
...
You might try writing the sequence as
a_(n+1) = a_n + a_(n-1)
saves using all those noisy words.
To find the first four terms of the recursively defined sequence, we start with the given initial values and then use the recursive formula to find the subsequent terms.
The given initial values are:
a_1 = 9
a_2 = 9
Now, we can use the recursive formula:
a_n+1 = a_n + a_n-1
Let's calculate the first four terms step by step:
Term 1 (a_1): We are given that a_1 = 9. So, the first term is 9.
Term 2 (a_2): We are given that a_2 = 9. So, the second term is also 9.
Term 3 (a_3): Using the recursive formula, we substitute n = 3:
a_3 = a_2 + a_1
= 9 + 9
= 18
Term 4 (a_4): Using the recursive formula, we substitute n = 4:
a_4 = a_3 + a_2
= 18 + 9
= 27
Therefore, the first four terms of the sequence are 9, 9, 18, 27.
So, the correct answer choice is D) 9, 9, 18, 27.