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A sequence has a₁ = 3 and an = 2a_(n-1) + 1 for n > 1…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A sequence has $a_1 = 3$ and $a_n = 2a_{n-1} + 1$ for $n > 1$ . Find $a_5$ and $a_8$ . Then add $1$ to each term and look for a pattern, and use it to guess a formula for $a_n$ .

Need a reminder? The key ideaShow

A sequence is a function on $1, 2, 3, \dots$ : a formula gives $a_n$ directly, a recurrence builds each term from earlier ones. The partial sum is $S_n = a_1 + \dots + a_n$ , with $a_1 = S_1$ and $a_n = S_n - S_{n-1}$ for $n \geq 2$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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A sequence has a₁ = 3 and an = 2a_(n-1) + 1 for n > 1…

The worked solution

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