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

No

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.