Find the first two terms a_1 =5 and an=3a _n-1+2
To find the first two terms of the sequence described by the formula an = 3an-1 + 2, we can use the recursive approach.
Given:
a1 = 5
an = 3an-1 + 2
Now, we can use the recursive formula to find the subsequent terms step by step.
To find the second term:
a2 = 3a1 + 2
Substitute the value a1 = 5 into the formula:
a2 = 3(5) + 2
= 15 + 2
= 17
Therefore, the second term a2 is equal to 17.
To find the third term:
a3 = 3a2 + 2
Substitute the value a2 = 17 into the formula:
a3 = 3(17) + 2
= 51 + 2
= 53
Therefore, the third term a3 is equal to 53.
Continuing this process, you can find the subsequent terms of the sequence. If you need to calculate more terms, follow the same steps: Substitute the value of the previous term into the formula to find the next term.