Question

Find an expression for the nth term (tn) in each of the following sequence:

2, 6, 10, 14, 18…

Answer 1

The answer is 34

Step-by-step explanation: I just have a big brain

Answer 2

Answer:
`t_n = 4n - 2`

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Work Shown:

The first term is a = 2 and the common difference is d = 4, since we're adding 4 to each term to get the next term.

`t_n = \text{nth term of arithmetic sequence}\\\\t_n = a+d(n-1)\\\\t_n = 2 + 4(n-1)\\\\t_n = 2 + 4n - 4\\\\t_n = 4n - 2`

Which is the answer.

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If you were to plug in say n = 3, then we get

`t_n = 4n - 2\\\\t_3 = 4(3) - 2\\\\t_3 = 12 - 2\\\\t_3 = 10`

showing that 10 is the third term, which matches with what the original sequence shows. I'll let you check the other values of n to fully confirm the answer.