A sequence of numbers is defined by the expression a(subscript n) = 3n + n^2
Which sequence corresponds to this expression?
A)4, 9, 12, 20
B)4, 10, 18, 28
C)4, 10, 15, 20
D)5, 10 ,15 20
Question:
What am I supposed to do here?
How would I solve this?
replace the expression with
n = 1 , 2, 3, and 4 and see which sequence matches your results.
I will do one of them
if n = 2
a2 = 3(2) + 2^2 = 10
(that would be your second number)
To solve this question, you need to substitute various values of 'n' into the given expression, a(subscript n) = 3n + n^2, and see which sequence matches.
Let's try substituting 'n' with the first number from each option:
Option A:
For 'n' = 1, a(subscript n) = 3(1) + 1^2 = 4
For 'n' = 2, a(subscript n) = 3(2) + 2^2 = 10
For 'n' = 3, a(subscript n) = 3(3) + 3^2 = 18
For 'n' = 4, a(subscript n) = 3(4) + 4^2 = 28
Option B:
For 'n' = 1, a(subscript n) = 3(1) + 1^2 = 4
For 'n' = 2, a(subscript n) = 3(2) + 2^2 = 10
For 'n' = 3, a(subscript n) = 3(3) + 3^2 = 18
For 'n' = 4, a(subscript n) = 3(4) + 4^2 = 28
Option C:
For 'n' = 1, a(subscript n) = 3(1) + 1^2 = 4
For 'n' = 2, a(subscript n) = 3(2) + 2^2 = 10
For 'n' = 3, a(subscript n) = 3(3) + 3^2 = 15
For 'n' = 4, a(subscript n) = 3(4) + 4^2 = 20
Option D:
For 'n' = 1, a(subscript n) = 3(1) + 1^2 = 4
For 'n' = 2, a(subscript n) = 3(2) + 2^2 = 10
For 'n' = 3, a(subscript n) = 3(3) + 3^2 = 15
For 'n' = 4, a(subscript n) = 3(4) + 4^2 = 20
Comparing the results of each substitution, we see that Option C: 4, 10, 15, 20 corresponds to the given expression, a(subscript n) = 3n + n^2.
Therefore, the answer is C) 4, 10, 15, 20.