By starting with a million and alternatively dividing by 2 and multiplying by 5, Anisha created a sequence of integers that starts 1000000, 500000, 2500000, 1250000, and so on. What is the last integer in her sequence? Express your answer in the form \(a^b\), where a and b are positive integers and a is as small as possible.
Thanks :)
I think your sequence DIVERGES and does not converge !!
1,000,000, 500,000, 2,500,000, 1,250,000, 6,250,000, 3,125,000, 15,625,000.....and blows up!!!
Make sure that you have stated the question accurately. If you were to start with a 1,000,000 and DIVIDE by 5, then MULTIPLY by 2, then it would CONVERGE to something. But, NOT the way the question is stated !!.
I think what he/she means is: What is the last WHOLE INTEGER ??? If that is what is meant, then:
1,000,000, 500,000, 2,500,000, 1,250,000, 6,250,000, 3,125,000,15,625,000, 7,812,500, 39,062,500, 19,531,250, 97,656,250, 48,828,125, 244,140,625.
The last WHOLE INTEGER is =244,140,625 =5^12
+118608 By starting with a million and alternatively dividing by 2 and multiplying by 5, Anisha created a sequence of integers that starts 1000000, 500000, 2500000, 1250000, and so on. What is the last integer in her sequence? Express your answer in the form , where a and b are positive integers and a is as small as possible.
You start with \(10^6\) which is \( 5^6 * 2^6 \)
After you have divided this by 2 six times you will not be able to divide it by 2 any more, not if you want an integer answer.
So the last integer term will be \(\frac{5^6 * 2^6}{2^6} * 5^6 = 5^{12}\)
