Cambridge International Mathematics

5 28 students go tramping. 23 get sunburn, 8 get blisters, and 5 get both sunburn and blisters. Determine the probability that a ...

MV noMV computer 124 168 no computer 16 22 1 3 023 6 4675 9 12 number of days number of clients O Review set 25A #endboxedheadin ...

back side vowel vowel vowel consonant consonant consonant 1st draw 2nd draw Review set 25B #endboxedheading Age Frequency 0 - 19 ...

Likes Dislikes Year 8 129 21 Year 9 108 42 Year 10 81 69 8 A class consists of 25 students. 15 have blue eyes, 9 have fair hair, ...

Sequences 26 Contents: A Number sequences [2.12] B Algebraic rules for sequences [2.12] C Geometric sequences [2.12] D The diffe ...

Anumber sequenceis a set of numbers listed in a specific order, where the numbers can be found by a specific rule. The first ter ...

, , , ..... , , , ..... , , , ..... , , , , ..... , , , , ..... EXERCISE 26A 1 Write down a rule to describe the sequence and he ...

The possible substitutions fornare: n=1, 2 , 3 , 4 , 5 , 6 , ...... so an algebraic rule forunis valid for n 2 Z+only. Example 3 ...

EXERCISE 26B 1 Find the firstfourterms of the sequence withnth term: a un=2n+3 b un=2n+5 c un=3n+2 d un=3n+5 e un=¡ 2 n+1 f un=¡ ...

We see that u 1 =2£ 30 u 2 =2£ 31 u 3 =2£ 32 u 4 =2£ 33 so each time the power of 3 is one less than theterm number. So, a gener ...

We have seen that alinearsequence is one in which each term differs from the previous term by the same constant. The general ter ...

We again construct a difference table, and this time we include another row for thesecond difference ¢2. This is the difference ...

² For thecubic sequence un=an^3 +bn^2 +cn+d, thethird differencesare constant and equal to 6 a. The general difference table is: ...

b u 1 =1, u 2 =3, u 3 =6, u 4 =10, u 5 =15, u 6 =21 The difference table is: n 123456 un 136101521 ¢1 234 5 6 ¢2 11 1 1 The¢2val ...

EXERCISE 26D 1 Use the method of differences to find the general termunof: a 1 , 5 , 9 , 13 , 17 , 21 , ...... b 17 , 14 , 11 , ...

7 Consider the pattern: a Supposeunis the number of squares contained in thenth figure, sou 1 =2andu 2 =6+2=8. Find the values o ...

9 Consider the sequence 6 , 24 , 60 , 120 , 210 , 336 , ...... a Use the difference method to find the general term un. b Sugges ...

8 Use the method of differences to find the general term un of: a 43 , 34 , 25 , 16 , 7 , ...... b 4 , 12 , 22 , 34 , 48 , ..... ...

Circle geometry 27 Contents: A Circle theorems [4.7] B Cyclic quadrilaterals [4.7] Opening problem #endboxedheading The towns of ...

² Anarcof a circle is any continuous part of the circle. ² Achordof a circle is a line segment joining any two points on the cir ...