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Expert: Robi Bhattacharjee - 8/20/2008


Question
what is the nth term for the following sequence? and please eplain.

2 4 16 256

Answer
Hi Kyle,

The following sequence seems to square each time. Observe that 2 squared is 4, 4 squared is 16, and 16 squared is 256. But you want the nth term. So why don't we write each of these as a power of 2.

2 = 2 ^ 1

4 = 2 ^ 2

16 = 2 ^ 4

256 = 2 ^ 8.


Do you see a pattern in 1 , 2 , 4 , 8? If we can observe an nth term in this sequence, then our original problem will simply be 2 ^ (that nth term).

Again, lets use exponents of two.

1 = 2 ^ 0

2 = 2 ^ 1

4 = 2 ^ 2

8 = 2 ^ 3.

By observing this we obtain that nth term is 2 ^ (n - 1)


so the answer to our original problem is 2 ^ ( 2 ^ (n - 1))


I hope this helped,

Robi

Feel free to ask me anytime.

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Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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