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 3and 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.