• Nie Znaleziono Wyników

# 1. An arithmetic sequence has first term a and common difference d, d ≠ 0. The 3rd, 4

N/A
N/A
Protected

Share "1. An arithmetic sequence has first term a and common difference d, d ≠ 0. The 3rd, 4"

Copied!
1
0
0

Pełen tekst

(1)

IB Questionbank Mathematics Higher Level 3rd edition 1

1. An arithmetic sequence has first term a and common difference d, d ≠ 0.

The 3rd, 4th and 7th terms of the arithmetic sequence are the first three terms of a geometric sequence.

(a) Show that a = d 2

3 .

(3)

(b) Show that the 4th term of the geometric sequence is the 16th term of the arithmetic sequence.

(5) (Total 8 marks)

2. Find the sum of all three-digit natural numbers that are not exactly divisible by 3.

(Total 5 marks)

3. An 81 metre rope is cut into n pieces of increasing lengths that form an arithmetic sequence with a common difference of d metres. Given that the lengths of the shortest and longest pieces are 1.5 metres and 7.5 metres respectively, find the values of n and d.

(Total 4 marks)

Cytaty

Powiązane dokumenty

Extending this idea we will introduce Hadamard matrices: such a matrix (of order q) gives sequences which can be generated by finite automata and which satisfy (2) where M 2 is

Compute terms of this sequence numbered from 3

If the matrix ½aij is nilpotent, then the algebra of constants k½X d is ﬁnitely generated.. u It turns out that the assumption of nilpotency of the matrix ½aij is

, b n , such that the products of their terms are equal has been considered by Gabovich [1], Mirkowska and Makowski [2], Szymiczek [5] and by Saradha, Shorey and Tijdeman [3, 4].. , b

The asymptotic behavior of the solutions of the n-th order differential equations have been considered by T.. Similar problems with regard to the second order

[r]

(6 points) An 81 metre rope is cut into n pieces of increasing lengths that form an arithmetic sequence with a common difference of d metres.. Given that the lengths of the shortest

This follows from the domain monotonic- ity of conformal radius (Schwarz’s lemma) and the following symmetrization result which is due to P´ olya, Szeg˝ o, Hayman and Jenkins (see