Problem of the Day
by aoum, Mar 5, 2025, 1:10 AM
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Problem of the Day (Math) - 3/4/25
In a certain sequence, each term after the first is obtained by multiplying the previous term by 2 and then adding 3. If the first term is 1, what is the value of the fifth term?
This is a simple, experimental problem. Starting tomorrow, the problems of the day will become more challenging and include various topics, including math, science, and coding.
In a certain sequence, each term after the first is obtained by multiplying the previous term by 2 and then adding 3. If the first term is 1, what is the value of the fifth term?
.This is a simple, experimental problem. Starting tomorrow, the problems of the day will become more challenging and include various topics, including math, science, and coding.
This post has been edited 3 times. Last edited by aoum, Mar 5, 2025, 2:28 AM
Reason: Solution Release
Reason: Solution Release
![\[a_{n+1}=2a_n+3\]](http://latex.artofproblemsolving.com/f/0/6/f066772ee42a31ca04e76cb9a992f854e221fec9.png)
so the general form is ![\[a_{n+1}=2(2(\cdots(2(1)+3)\cdots)+3)+3\]](http://latex.artofproblemsolving.com/d/c/8/dc8c61b255637308e9c1f48b0a0af4af1ca17987.png)
so ![\[a_{n+1}=2^na_1+\sum_{i=0}^{n-1}3\cdot2^i=2^{n-1}+3\cdot2^{n-1}=\boxed{2^{n+1}-3}\]](http://latex.artofproblemsolving.com/5/4/6/546a389d1ec75d43df8217e64bf023d6e6dab886.png)
Try out the harder problems of the day.
March 2025