Question

Show that the following numbers are in continued proportion:
(i) 48, 60, 75
(ii) 36, 90, 225
(iii) 16, 84, 441

Answer 1

(i) 48:60, 60:75
Product of means = 60 × 60 = 3600
Product of extremes = 48 × 75 = 3600
Product of means = Product of extremes
Hence, 48:60::60:75 are in continued proportion.

(ii) 36:90, 90:225
Product of means = 90 × 90 = 8100
Product of extremes = 36 × 225 = 8100
Product of means = Product of extremes
Hence, 36:90::90:225 are in continued proportion.

(iii) 16:84, 84:441
Product of means = 84 × 84 = 7056
Product of extremes = 16 × 441 = 7056
Product of means = Product of extremes
Hence, 16:84::84:441 are in continued proportion.