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05 Nov 2014, 23:49
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Given AP - 1,4,7,10,13,16,19,22,25,28,31,34,37,40,43,46 …
If the first number of the progression "a", the last number of the progression "k" and the common difference "d" is given then the number of items in the progression
□ Including the first and last numbers is given by n = [(a+k)/d] + 1 e.g.: n = ((1+46)/3) +1= 15+1=16
□ Including at least one of the numbers is given by n = [(a+k)/d] e.g.: n = ((1+46)/3) = 15=15
□ Excluding the first and last numbers is given by n = [(a+k)/d] - 1 e.g.: n = ((1+46)/3)−1= 14
If you notice, the fractional value is rounded off by truncating the decimal altogether. Is that how it should be done? Or should I round off to the closest integer basing on the rounding principles?
Thanks in advance for all the help!
If the first number of the progression "a", the last number of the progression "k" and the common difference "d" is given then the number of items in the progression
□ Including the first and last numbers is given by n = [(a+k)/d] + 1 e.g.: n = ((1+46)/3) +1= 15+1=16
□ Including at least one of the numbers is given by n = [(a+k)/d] e.g.: n = ((1+46)/3) = 15=15
□ Excluding the first and last numbers is given by n = [(a+k)/d] - 1 e.g.: n = ((1+46)/3)−1= 14
If you notice, the fractional value is rounded off by truncating the decimal altogether. Is that how it should be done? Or should I round off to the closest integer basing on the rounding principles?
Thanks in advance for all the help!
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06 Nov 2014, 10:41
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In your expressions, it needs to be the difference between k and a, not their sum. You should not be getting any fractional values in the expressions. Also, no need to burden your brain with the additional variations, that is just too much to keep track in the exam. Just stick with the following expression for the arithmetic sequences:
# of Terms = [(Last Term - First Term)/Spacing] + 1
Here the difference between the first and last term gives us the total distance between the end points. When we divide it by the spacing it gives us the number of gaps between the terms, we add one to then give us the number of terms.
Cheers,
Dabral
# of Terms = [(Last Term - First Term)/Spacing] + 1
Here the difference between the first and last term gives us the total distance between the end points. When we divide it by the spacing it gives us the number of gaps between the terms, we add one to then give us the number of terms.
Cheers,
Dabral
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
