Identify the Sequence 2 , -4 , 6 , -8 , 10

Problem

2,−4,6,−8,10,…

Solution

1. Observe the absolute values of the terms in the sequence, which are $2, 4, 6, 8, 10$.

2. Identify that these absolute values represent the sequence of even numbers, which can be written as 2*n for n=1,2,3,…

3. Determine the pattern of the signs, which alternate starting with a positive value: +,−,+,−,+

4. Apply the alternating factor (−1)^(n+1) to account for the signs starting with a positive first term.

5. Combine the alternating factor and the even number expression to find the general term (a_n)

Final Answer

(a_n)=(−1)^(n+1)*(2*n)

Want more problems? Check here!