Theory question 109
Progressions(a) What is the 25th term of 5, 9, 13……..?
(b) Find the 5th term of 8/9, −4/3, 2 ………
(c) The 3rd and 6th terms of a Geometric Progression (G.P) are 48 and 14 2/9 respectively. Write down the first four terms of the G.P.
Show the model answer
Model answer
(a) A.P. with a = 5, d = 4: T25 = 5 + 24 × 4 = 101
(b) G.P. with a = 8/9, r = (−4/3) ÷ (8/9) = −3/2
T5 = 8/9 × (−3/2)4 = 8/9 × 81/16 = 9/2 = 4½
(c) ar2 = 48 and ar5 = 128/9
Divide: r3 = 128/432 = 8/27, so r = 2/3
a = 48 ÷ 4/9 = 108
First four terms: 108, 72, 48, 32
Explanation
Dividing two terms of a G.P. removes a and leaves a power of r.