Answer:
The first five values are 12, 14, 16, 18 and 20
The recursive formula is as follow
[tex]\left \{ {{a_{1} =12} \atop {a_{n} =a_{n-1} } + 2} \right.[/tex]
Step-by-step explanation:
Since we need to find the first 5 values we start with n = 1 to n = 5. Note that we don't start from n = 0 as the question states that n ≥ 1.
For the first 5 values we just replace the value of n with 1, 2, 3, 4 and 5 and calculate the answer
[tex]a_{1} = 2(1) + 10 = 12\\ a_{2} = 2(2) + 10 = 14\\ a_{3} = 2(3) + 10 = 16\\ a_{4} = 2(4) + 10 = 18\\ a_{5} = 2(5) + 10 = 20[/tex]
The first five values are 12, 14, 16, 18 and 20
A recursive formula is one that
a) Mentions the initial term
b) provides a formula connecting the previous term to the existing term.
Since we know the first term is 12, i.e [tex]a_{1} = 12[/tex] and we know that the difference between consecutive terms is 2 we can conclude that the recursive formula is made up of the following two formulas
[tex]a_{1} = 12[/tex]
[tex]a_{n} = a_{n-1} + 2[/tex]
The over all formula is as follow
[tex]\left \{ {{a_{1} =12} \atop {a_{n} =a_{n-1} } + 2} \right.[/tex]
