Arithmetic and geometric sequences and series

Learning objectives

Identify an arithmetic sequence, find the common difference, and use uₙ = u₁ + (n − 1)d and Sₙ = ½n(2u₁ + (n − 1)d) to find terms, sums and the number of terms

Identify a geometric sequence, find the common ratio, and use uₙ = u₁r^(n − 1) and Sₙ = u₁(rⁿ − 1)/(r − 1) to find terms and sums

Decide from data whether an arithmetic or a geometric model is more appropriate, by checking whether successive differences or successive ratios are roughly constant

Use technology to solve for n, for example to find how many terms are needed before a sum passes a given value, and interpret a non-integer solution correctly

Apply sequences to real contexts such as seating rows in a theatre, salary increments, population growth and the total distance covered by a bouncing ball

Recognise that spreadsheets and calculator list features can generate and sum a sequence, and use them to check an algebraic answer