Annsgrayidn
Answered

From health tips to tech hacks, find it all on IDNLearn.com. Find reliable solutions to your questions quickly and easily with help from our experienced experts.

please help!

Given an arithmetic progression -8, -3, 2,.... Determine three consecutive terms in this progression which sum up to 111.​

Sagot :

Mhanifaidn

Answer:

  • 9th, 10th and 11th terms; 32, 37 and 42

=============================

Given AP:

  • -8, - 3, 2, ...

We observe that:

  • The first term is a = - 8,
  • The common difference is d = -3 - (-8) = 2 - (-3) = 5.

Let the three terms be aₙ, aₙ₊₁, aₙ₊₂.

Use nth term formula:

  • aₙ = a + (n - 1)d = - 8 + (n - 1)*5 = - 8 + 5n - 5 = 5n - 13

The following two terms are:

  • aₙ₊₁ = 5n - 13 + 5 = 5n - 8
  • aₙ₊₂ = 5n - 8 + 5 = 5n - 3

Their sum is 111, set an equation and solve for n:

  • 5n - 13 + 5n - 8 + 5n - 3 = 111
  • 15n - 24 = 111
  • 15n = 135
  • n = 135/15
  • n = 9

The three terms are 9th, 10th and 11th terms and they are:

  • 5*9 - 13 = 45 - 13 = 32
  • 32 + 5 = 37
  • 37 + 5 = 42
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com is your source for precise answers. Thank you for visiting, and we look forward to helping you again soon.