Answer:
The sequence 3 , 4 , 6 , 10 , 18 described by the 2nd term is t2 = 4 and recursive definition is tn+1 = 2 tn - 2 ⇒ 4th answer
Step-by-step explanation:
* Lets revise the recursive formula
1. Determine if the sequence is arithmetic (Do you add, or subtract, the
same amount from one term to the next?)
2. Find the common difference. (The number you add or subtract.)
3. Create a recursive formula by stating the first term, and then stating
the formula to be the previous term plus the common difference.
a1 = first term;
an+1= an + d
- Where:
# a1 = the first term in the sequence
# an = the nth term in the sequence
# an+1 = the term after the nth term
# n = the term number
# d = the common difference.
* Now lets solve the problem
∵ The recursive definition is tn+1 = 2 tn - 2 and t2 = 4
- Look to the answer we have three answer with second term = 4,
1st , 2nd and 4th
- Lets find the 1st term
∵ t2 = 2 t1 - 2
∵ t2 = 4
∴ 4 = 2 t1 - 2 ⇒ add 2 to the both sides
∴ 6 = 2 t1 ⇒ divide the two sides by 2
∴ t1 = 3
- We have two answer with first term = 3, 2nd and 4th answers
* Lets find the third term
∵ t3 = 2 t2 - 2
∵ t2 = 4
∴ t3 = 2 (4) - 2 = 8 - 2 = 6
∴ The 4th answer has the third term = 6
* The 4th sequence 3 , 4 , 6 , 10 , 18 described by the 2nd term is
t2 = 4 and recursive definition is tn+1 = 2 tn - 2
= 1/2