Question

Each sequence below gives an explicit formula. Write the first five terms of each sequence. Then, write a recursive

Answer 1

Answer:

The first five values are 12, 14, 16, 18 and 20

The recursive formula is as follow

$\left \{ {{a_{1} =12} \atop {a_{n} =a_{n-1} } + 2} \right.$

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

$a_{1} = 2(1) + 10 = 12\\ a_{2} = 2(2) + 10 = 14\\ a_{3} = 2(3) + 10 = 16\\ a_{4} = 2(4) + 10 = 18\\ a_{5} = 2(5) + 10 = 20$

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 $a_{1} = 12$ 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

$a_{1} = 12$

$a_{n} = a_{n-1} + 2$

The over all formula is as follow

$\left \{ {{a_{1} =12} \atop {a_{n} =a_{n-1} } + 2} \right.$