Theory question 113
Progressions(a) How many numbers between 75 and 500 are divisible by 7?
(b) The 8th term of an Arithmetic Progression (A.P) is 5 times the third term while the 7th term is 9 greater than the 4th term. Write the first five terms of the A.P.
Show the model answer
Model answer
(a) The multiples of 7 run from 77 (7 × 11) to 497 (7 × 71): 71 − 11 + 1 = 61 numbers.
(b) a + 7d = 5(a + 2d) → 4a = −3d. (a + 6d) − (a + 3d) = 9 → d = 3, so a = −9/4.
First five terms: −2¼, ¾, 3¾, 6¾, 9¾.
Explanation
Count multiples of 7 as an AP from 77 to 497 with difference 7.