annsgray
Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

please help!

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

Sagot :

mhanifa

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
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.