Help With Patterns

• Arithmetic Patterns
  • When the pattern has a common difference.
  • Example: 1, 6, 11, 16 .... The common difference is 5. The next term would be 21.
  • How can we find the 15th term? 1,6,11,16........................15th term
  • The first no. + ( the number of the rest of the terms x common difference)
    1 + { (14) x (5) } = 71

   

• Geometric Patterns
  • Geometric patterns have common ratios.
  • Example: 7, 21, 63 .....What do we have to multiply by 7 to get 21?-- 7(x) = 21 --- 3--- common ratio. How can we find the 8th term?
  • Take your calculator put in 3 (the common ratio) and multiply it by the 7 = 21. It is important that you put the ratio in the calculator first.
  • You now have gone 2 places in the pattern. Now push the = sign on the calculator 6 more times. This will take you to the 8th term of the pattern. The calculator should read 15309. This is the 8th term in our example pattern.

   

• Repeating Decimal Patterns
  • When the pattern is a repeating decimal
  • Example:  .456456456  How can we find the 46th number of this repeating decimal?
  • To obtain the 46th number divide 3 into 46. You get 15 with 1 remainder.
  •  The answer is a 4, or 5, or 6.  With 1 remainder count one number over in the series which gives you a 4.-----no remainder the answer would be 6 and with a remainder of 2 the answer would be 5.