Question
What would be the $178^{\text{th}}$ term in the following series?
2, 5, 8, 11, 14, ...
This question was previously asked in
RRB ALP 2018 CBT 2 Fitter Question Paper (21-Jan-2019) (Shift 3)
The correct answer is
533
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.
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