IB Maths AI HL 1.2 Arithmetic sequences and series Question Bank

Practise IB Maths AI HL 1.2 through questions that extend arithmetic sequences to parameters, multi-step sums and applied growth or decay models.

Exam points

Solve HL arithmetic-sequence problems with parameters, recurrence links and multi-step finite-sum reasoning.
Translate applied growth, decay or threshold contexts into a justified arithmetic model and solve it accurately.
Compare equivalent forms, check domain and index restrictions, and interpret the result in context.

[Maximum number: 5]

A bakery sells egg tarts in boxes. Each box contains 6 tarts. On a particular morning, the bakery has 400 freshly baked tarts. The number of tarts remaining, after n boxes have been sold, forms an arithmetic sequence, $u_{n}=u_{1}+(n-1) d$ .

(a)

Write down the value of d.

[ 1 ]

(b)

Find the value of $u_{1}$ .

[ 1 ]

(c)

Find the greatest number of boxes the bakery can sell that morning.

[ 3 ]

attempt to solve $394-6(n-1) \geq 0$ OR $400 \div 6$

Note: Accept equality or any inequality with zero seen, graphical approach to find zero, use of table/list to find zero.
( n< ) $66.6666 \ldots$
( n= ) 66
(A1)
A1

Note: If 400 is given as the answer in (b) then n=67 in part (c).

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SL 1.2—Arithmetic sequences and series question 1

Question (a)

Question (b)

Question (c)