2, 5, 8, 11, 14, ...
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.
Important Questions from Progression (Notes)
- The sum of 16 terms of the series $\sqrt{2} + \sqrt{8} + \sqrt{18} + \sqrt{32} + .....$ is :
- A pilgrim starts walking for a journey of 115 km. On the first day he covers 7 km, the next day 9 km, and likewise keeps adding 2 km everyday till he reaches 15 km per day which he maintains for the rest of the journey. How many days in all will he take to complete the journey?
If a, b and c are in Geometric Progression and $a^\frac{1}{x} = b^\frac{1}{y} = c^\frac{1}{z}$ then, x, y, z are in ________.
Which of the following statement is true about the geometric series
$ 1 + r +r^2 + r^3 + ...............; (r > 0) $?
$6240$ रुपये की राशि $30$ किस्तों में इस प्रकार चुकाई जाती है कि प्रत्येक किस्त पिछली किस्त से $10$ रुपये अधिक है । पहली किस्त की मूल्य ____________है।
