Assessment: Sequences and Series

What is the difference between a sequence and a series?

What defines a geometric progression?

An A.P. has a₁=10 and d=−3. Find the 7th term.

Find the sum of the first 3 terms of the G.P. with a₁=4 and r=2.

An A.P. has a₁=6, d=4. Find the sum of the first 12 terms.

Find the sum of 20 + 5 + 1.25 + ... continuing forever.

A theatre's rows have seats increasing by 3 per row, starting at 15 seats in row 1. How many seats are in row 6?

An investment of $2000 grows by a factor of 1.1 each year. Find its value after 3 years (i.e. a₄, since a₁ is the initial value).

How is the geometric series sum formula, Sₙ=a₁(1−rⁿ)/(1−r), actually derived?

Convert the repeating decimal 0.777... to a fraction using the infinite geometric series formula (a₁=0.7, r=0.1). Give the answer as a fraction's numerator over 9 (just the numerator).