Question

The first terms of an arithmetic sequence are 5, 9, 13, 17, ... Determine whether or not 116 is a term in this sequence.​

Answer 1

Answer:

It is not

Step-by-step explanation:

...101, 105, 109, 113, 117

Answer 2

Answer:

No

Step-by-step explanation:

116 = 5 + (n-1)4  We take the initial value of 5 and we add that to the n-1 which represent 1 minus the number in the sequence that 116 is at times how much the sequence increase with each term.

Solve to see if n is a whole number

116 = 5 + 4n -4  Distribute the 4

116 = 4n + 1 combine like terms

115 = 4n  subtract 1 from both sides of the equation

n = 28.75  Divide both sides by 4

I cannot have a 28.75 step so 116 cannot be an answer.