Theory question 106
Fractions, Decimals and Approximation(a) If 17x = 3752 − 3562, find the exact value of x.
(b) If 4x = 21/2 × 8, find x.
(c) The sum of the first 9 terms of an A.P. is 72 and the sum of the next 4 terms is 71. Find the A.P.
Show the model answer
Model answer
(a) Difference of two squares: 3752 − 3562 = (375 − 356)(375 + 356) = 19 × 731 = 13889
x = 13889 ÷ 17 = 817
(b) 22x = 21/2 × 23 = 27/2, so 2x = 7/2 and x = 7/4
(c) S9 = 9/2(2a + 8d) = 72, so a + 4d = 8
S13 = 72 + 71 = 143 = 13/2(2a + 12d), so a + 6d = 11
Subtract: 2d = 3, d = 3/2; then a = 8 − 6 = 2
The A.P. is 2, 3½, 5, 6½, 8, …
Explanation
The first 13 terms add up to 72 + 71 = 143; use the sum formula twice.