Theory question 109
Progressions(a) In an A.P. the difference between the 8th and the 4th terms is 20 and the 8th term is 1½ times the fourth term. What is the: (i) common difference, (ii) first term of the sequence? (b) The value of a machine depreciates each year by 5% of its value at the beginning of that year. If its value when new on 1st January, 1980 was N10,250.00, what was its value in January, 1989 when it was 9 years old? Give your answer, correct to three significant figures
Show the model answer
Model answer
(a)(i) (a + 7d) − (a + 3d) = 4d = 20 ⇒ d = 5.
(ii) a + 7d = 1½(a + 3d) ⇒ a + 35 = 1.5a + 22.5 ⇒ 0.5a = 12.5 ⇒ a = 25.
(b) Value = 10 250 × (0.95)9 = 10 250 × 0.6302 = N6 460 (3 s.f.).
Explanation
Depreciation of 5% a year means multiplying by 0.95 each year.