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Sequences and Series

Finding the nth Term


Guess the next term of the following sequence:

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

What is the 6th6 ^{th} term of the sequence {n2+2n+8}n=1? \{ n^2 + 2 n + 8 \}_{n=1}^\infty?

The first nn terms of a sequence sum to n(n+2)(2n+1)n(n+2)(2n+1). What is the value of the 6th6 ^{th} term?

The sequence {an}\{a_n\} satisfies a1=1a_1=1 and an+1=11nan for n1. a_{n+1}=11 ^n a_n \text{ for } n \geq 1.

For what value of kk do we have ak=11276a_k=11 ^{276}?

If {an}\{a_n\} is an arithmetic progression with a11=133a_{11}=133 and a23=313a_{23}=313, what is a50a_{50}?


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