Waste less time on Facebook — follow Brilliant.
×
Back to all chapters

Sequences and Series

What's the sum of the first 100 positive integers? How about the first 1000?

Finding the nth Term

         

Guess the next term of the following sequence:

\[ 2, \quad 3, \quad 5, \quad 8, \quad 12, \quad 17, \quad \square \]

What is the \(6 ^{th}\) term of the sequence \( \{ n^2 + 2 n + 8 \}_{n=1}^\infty?\)

The first \(n\) terms of a sequence sum to \(n(n+2)(2n+1)\). What is the value of the \(6 ^{th}\) term?

The sequence \(\{a_n\}\) satisfies \(a_1=1\) and \[ a_{n+1}=11 ^n a_n \text{ for } n \geq 1.\]

For what value of \(k\) do we have \(a_k=11 ^{276}\)?

If \(\{a_n\}\) is an arithmetic progression with \(a_{11}=133\) and \(a_{23}=313\), what is \(a_{50}\)?

×

Problem Loading...

Note Loading...

Set Loading...