Identify the Series Type

The given series is 2, 5, 8, 11, 14, ...

This is an arithmetic series because the difference between consecutive terms is constant.

• First term ($a_1$): $2$
• Common difference ($d$): $5 - 2 = 3$

Arithmetic Series Formula

The formula to find the $n^{\text{th}}$ term ($a_n$) of an arithmetic series is:

$ a_n = a_1 + (n-1)d $

Calculate the 178th Term

We need to find the $178^{\text{th}}$ term, so $n = 178$.

Substitute the values into the formula:

$ a_{178} = 2 + (178-1) \times 3 $

$ a_{178} = 2 + (177) \times 3 $

$ a_{178} = 2 + 531 $

$ a_{178} = 533 $

Conclusion

The $178^{\text{th}}$ term in the series is 533.