There's an easier way than adding!

Algebra Level pending

There is a series of numbers that goes like this:

1, 5, 9, 13, 17, 21.........

If this series of numbers go on and on, what will the 25th number be?

The answer is 97.

2 solutions

Rina Kajitani
Nov 1, 2014

1+4(25-1)

This is how I learned how to do it!

Venture Hi
Oct 31, 2014

a(n)=a(1)+(n-1)d where a(1) is the first term, a(n) is the n-th term, and d=arithmetic difference

Sorry, I guess I'm too young to understand your equation... Can you explain it a bit more?

Rina Kajitani - 6 years, 7 months ago

I'm actually still 11, so maybe that's the reason I don't understand?

Rina Kajitani - 6 years, 7 months ago

@Rina Kajitani I'll explain. The formula for finding the $n^{th}$ term is $a + (n - 1)\times d$ where $n$ is the term which has to be found. $a$ is the first term of the series and $d$ is the common difference between $2$ consecutive terms. I hope you understood it.

Anuj Shikarkhane - 6 years, 7 months ago

Thanks! I think I understand now. What you're trying to say is that your adding the common difference n-1 times, right? And then if you add the first number, it will be the sum of all the numbers from 1 to the 25th number. Yeah, I got it now. Again, thanks for the explanation!!!

Rina Kajitani - 6 years, 7 months ago

There's an easier way than adding!

The answer is 97.

2 solutions

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