Sequences and Series

Sequences Warmup


If {an}\{a_n\} is a sequence defined by an=n2+n+1a_n = n^2 + n + 1 for each natural number nn, what is a5?a_5?

Suppose {an}\{a_n\} is a sequence defined by a1=1,a2=1,a_1 = 1, a_2 = 1, and an=an1+an2a_n = a_{n-1} + a_{n -2} for each natural number n>2.n > 2.

What is a6a_6?

A geometric progression is a sequence in which an=ran1a_n = r \cdot a_{n-1} for each natural number n>1n > 1, where rr is a real number called the common ratio.

If ana_n is a geometric progression with a1=5a_1 = 5 and a6=160a_6 = 160, what is a3a_3?

On Day 1, Isabel has $200 in the bank, and she adds $5 at the start of each subsequent day. On what day will her account’s value reach $300?

Each day this week, Morgan had twice as much money as the day before. On Day 6, Morgan had $40. How many dollars did Morgan have on Day 1?


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