Question

In an A.P sum of three consecutive terms is 27 and their product is 504. Complete the following activity to find the terms.

Activity:

Let three consecutive terms be a – d, a, a + d.

∴ a – d + a + a + d = `square`

∴ a = `square`

Similarly:

(a – d) × a × (a + d) = `square`

∴ [(9)² – d²] × 9 = 504

∴ (81 – d²) × 9 = 504

∴ d² = 81 – `square`

∴ d = ± 5

Thus by puting a = 9 and d = 5 we get three consecutive terms = `square`

Or by putting a = 9 and d = –5 we get three consecutive terms = `square`

Answer 1

Activity:

Let the three consecutive terms be a – d, a, a + d.

∴ a – d + a + a + d = \[\boxed{27}\]

∴ a = \[\boxed{9}\]

Similarly:

(a – d) × a × (a + d) = \[\boxed{504}\]

∴ [(9)² – d²] × 9 = 504

∴ (81 – d²) × 9 = 504

∴ d² = 81 – \[\boxed{56}\]

∴ d = ± 5

Thus by puting a = 9 and d = 5 we get three consecutive terms = \[\boxed{4, 9, 14}\]

Or by putting a = 9 and d = –5 we get three consecutive terms = \[\boxed{14, 9, 4}\].