Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Sequences & Series - Geometric - the General term.
Test Yourself 2.


 

Finding a term 1. Show (without writing out all the terms of the series) that the 12th term of the geometric series 64 + 32 + 16 is 1/32. 2. If 2p + 1, 5p and 12p - 4 are the first three terms in a geometric sequence, find the value of p and hence find the nth term.

Answer.p = 2 and Tn = 5×2n-1.
  3. Which expression is a term in the geometric series 3x - 6x2 + 12x3 ...?

(a) 59049x10.

(b) 2048x11

(c) 4096x12

(d) 531414x12.

AnswerT9 = 0.00001.

 4. Find the 9th term in the series:

1000, 100, 10, 1...

Express your answer as a decimal.

Answer(c).
Finding a 1st term 5. 6.
Finding a ratio. 7.

Answerx = +√6 or -√6.

 8.
Finding the number of terms 9. For the geometric series beginning

18 + 9 + 4.5

which term is that with a value just greater than 0.001?

Answern = 15.1 so to stop before 0.001 is the 15th term.

 10.
Given 2 terms 11. The third term of a geometric series is 36 and the sixth term is 972.

Find the common ratio and the first term of the series.

Answer.Ratio is 3
and the 1st term is 4.

 12.
     
Miscellaneous

15. The terms 2 + x + 3 form a geometric series.

Find the possible values of x.

  
  17. The numbers 2 - x, x and 5 - x form a geometric sequence.

What is the value of x?

Answer.x = 10/7.

18.
  19. 20.