Geometric Series KUS objectives BAT you need to

Geometric Series • KUS objectives BAT you need to be able to spot patterns to work out the common ratio and rule for a Geometric Sequence BAT use Percentages in Geometric Sequences BAT apply logarithms to solve problems Starter: Describe the recurrence relation for each sequence (formula for the next term)

WB 1 Common ratio Find the common ratio in each of these sequences:

WB 2 Nth term In a Geometric sequence, the nth term comes from multiplying the first term by the common ration (n – 1) times a, ar, 1 st Term 2 nd Term ar 2, ar 3, 3 rd Term 4 th Term …, nth Term For example. find the nth term of these: arn-1

WB 3 nth term Find the nth and 10 th terms of the following sequences…

WB 4 Finding a and r The second term of a Geometric sequence is 4, and the 4 th term is 8. Find the values of the common ratio and the first term 1 2 nd Term 2 4 th Term 2 ÷ 1 Square root Sub r into 1 Divide by √ 2 Rationalise

WB 5 ab finding a and r a) A geometric sequence has third term 12 and sixth term -96 Find the first term and the common ratio b) The third term of a geometric sequence is 324 and the fifth term is 36 Find the first term and the two possible values of the common ratio

WB 5 c finding a and r c) The numbers 3, x, and (x + 6) form the first three terms of a positive geometric sequence. Calculate the 15 th term of the sequence First term = 3 Common Ratio = 2 Nth term = 3 x 2 n-1 15 th Term = 3 x 214 x has to be positive 15 th Term = 49152

WB 6 using logarithms Find the first term in the geometric sequence 1, 3, 9, 27 … to exceed the value of 10000

WB 7: logarithms a) What is the first term in the sequence 3, 6, 12, 24… to exceed 1 million?

Using percentage change If I was to increase an amount by 10%, what would I multiply the value by? 1. 1 If I was to increase an amount by 17%, what would I multiply by? 1. 17 If I was to increase an amount by 10%, every year for 6 years, what would I multiply the value by? If I was to increase an amount by 17%, every year for 20 years, what would I multiply by?

WB 8 percentage change If £A is to be invested in a savings fund at a rate of 4%. How much should be invested so the fund is worth £ 10, 000 in 5 years? Y 1 Y 2 Y 3 Y 4 A Ar Ar 2 Ar 3 Ar 4 Ar 5 a= A r = 1. 04 Ar 5 = 10, 000 A x 1. 045 = 10, 000 A = £ 8219. 27 Y 5

• KUS objectives BAT you need to be able to spot patterns to work out the common ratio and rule for a Geometric Sequence BAT use Percentages in Geometric Sequences BAT apply logarithms to solve problems self-assess One thing learned is – One thing to improve is –

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