Math topic中文

Nth term

recognising and representing patterns/relationships by finding an algebraic expression for the nnth term

Practice questions

  1. 1Find the 8th term of the sequence 10, 11, 13, 16, 20,..., Answer
  2. 2The first four terms in a sequence of numbers are 3+k, 1+k, −1+k, −3+k, …3 + k,\ 1 + k,\ -1 + k,\ -3 + k,\ \dots where kk is a constant. Fin…
  3. 3Diagram 1 shows an equilateral triangle with sides of length 1 unit. An inverted white equilateral triangle with sides o…
  4. 4Study the pattern below. Write down the values of aa, bb and cc in Figure 11. Answer aa = ... bb = ... cc = ... Wr…
  5. 5The first four terms in a sequence of numbers are given below. Find T5T_5. Answer ... Find an expression, in terms of n,…
  6. 6Here are the first four terms of a sequence. 1351010715420\displaystyle \frac{13}{5}\quad \frac{10}{10}\quad \frac{7}{15}\quad \frac{4}{20}…
  7. 7In the following sequence, (1×2)−2=0(1\times2)-2=0 (2×3)−4=2(2\times3)-4=2 (3×4)−6=6(3\times4)-6=6 (4×5)−8=12(4\times5)-8=12 ... (a×12)−b=c(a\times12)-b=c ..…
  8. 8The figure shows the first three figures of a sequence formed by sticks of the same size. Find the number of small squar…
  9. 9The sum of the first n terms of a linear sequence is . Show that the sum of the first n terms in the sequence is always…
  10. 10The sequence T1,T2,T3,T4,…T_1, T_2, T_3, T_4,\dots has the following first four terms. T1=22−1=3T_1 = 2^2 - 1 = 3 T2=32−2=7T_2 = 3^2 - 2 = 7 T3=42−3=13T_3 = 4^2 - 3 = 13…
  11. 11The first four terms of a sequence are 5, 94\dfrac{9}{4}, 139\dfrac{13}{9}, 1716\dfrac{17}{16}. State the fifth term of the…
  12. 12In a sequence, each term is obtained by adding the same number from the previous term. The first four terms in a sequenc…
  13. 13The first four terms in a sequence of numbers are given below. T1=22+7T_1 = 2^2 + 7 T2=32+12T_2 = 3^2 + 12 T3=42+17T_3 = 4^2 + 17 T4=52+22T_4 = 5^2 + 22…
  14. 14The nth term of a sequence is given by Tn=6n−53nT_n = \frac{6n-5}{3n}. Use the formula to find T7T_7, giving your answer as an…
  15. 15Small triangles are formed by placing rods between dots as shown in the diagrams. Complete the table below. Explain why…
  16. 16The first five terms of a sequence are given below. 3278111815321950\frac{3}{2}\quad \frac{7}{8}\quad \frac{11}{18}\quad \frac{15}{32}\quad \frac{19}{50}…
  17. 17The first four terms of a sequence are 5, 9, 13 and 17. (a) Write down the 8th term of the sequence. Answer ... (b) Find…
  18. 18The numbers 1 to 100 are arranged in a table as shown below. A L-shaped shaded frame can be placed around various number…
  19. 19The first four terms in a sequence of numbers are given below. T1=32+5=14T_1 = 3^2 + 5 = 14 T2=42+8=24T_2 = 4^2 + 8 = 24 T3=52+11=36T_3 = 5^2 + 11 = 36…
  20. 20The table below shows a flooring consisting of square tiles measuring 1 m^2 each. Each day similar tiles are added to th…
  21. 21The diagram shows the first three of a sequence of figures that are formed by squares of the same size. The number of ve…
  22. 22(1×2) − 2 = 0 (2×3) − 4 = 2 (3×4) − 6 = 6 (4×5) − 8 = 12 ... (a×12)−b=c(a\times 12) - b = c ... (d×e)−f=g(d\times e) - f = g Find the v…
  23. 23The first four terms in a sequence of numbers, x1,x2,x3,x4,…x_1, x_2, x_3, x_4, \dots are given below. x1=2(0)+1=1x_1 = 2(0) + 1 = 1 x2=2(1)+3=5x_2 = 2(1) + 3 = 5…
  24. 24These are the first four terms of a sequence. 5/2 20/3 45/4 80/5 Write down the next two terms. Answer ..., ... Find an…
  25. 25These are the first four terms of a sequence. 4 12 36 108 Write down the 6th term of the sequence. Answer ___ Find an ex…
  26. 26A piece of A0-sized paper has a total surface area of 1 m^2. The length and breadth of the A0-sized paper are x m and y…
  27. 27Here are the first four terms of a sequence. 2, 53\frac{5}{3}, 105\frac{10}{5}, 177\frac{17}{7} Find the fifth term of the…
  28. 28Jane claims that the first three terms of the sequence 1, 2, 4, ... can also be represented by an expression that is dif…
  29. 29These are the first four terms of a sequence. 2 6 10 14 Find an expression, in terms of nn, for the nnth term of the s…
  30. 30The first four terms of a sequence are 27, 24, 21 and 18. Write down the 8th term of the sequence. Ans: ___ Find an expr…
  31. 31The first four terms in a sequence of numbers are given below. T1=52−18=7T_1 = 5^2 - 18 = 7 T2=62−22=14T_2 = 6^2 - 22 = 14 T3=72−26=23T_3 = 7^2 - 26 = 23…
  32. 32The first four terms in a sequence of numbers are given below. Complete the row in the above table for T5T_5. Find an ex…
  33. 33Sally is making square patterns with her square tiles using the pattern shown. She has black and white tiles. Find the s…
  34. 34Consider the sequence: T1=1=1T_1 = 1 = 1 T2=1+2=3T_2 = 1 + 2 = 3 T3=1+2+3=6T_3 = 1 + 2 + 3 = 6 T4=1+2+3+4=10T_4 = 1 + 2 + 3 + 4 = 10 T5=1+2+3+4+5=15T_5 = 1 + 2 + 3 + 4 + 5 = 15…
  35. 35The first four terms in a sequence of numbers are given below. T1=(1×3)+8=11T_1 = (1\times 3) + 8 = 11 T2=(2×4)+12=20T_2 = (2\times 4) + 12 = 20…