Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

find the smallest number of terms of the AP "-54,-52.5,-51,-49.5" ....that must be taken for the sum of the terms to be positive

Sagot :

oladayoademosu

The smallest number of terms of the AP that will make the sum of terms positive is 73.

Since we need to know the number for the sum of terms, we find the sum of terms of the AP

Sum of terms of an AP

The sum of terms of an AP is given by S = n/2[2a + (n - 1)d] where

  • n = number of terms,
  • a = first term and
  • d = common difference

Since we have the AP "-54,-52.5,-51,-49.5" ....", the first term, a = -54 and the second term, a₂ = -52.5.

The common difference, d = a₂ - a

= -52.5 - (-54)

= -52.5 + 54

= 1.5

Number of terms for the Sum of terms to be positive

Since we require the sum of terms , S to be positive for a given number of terms, n.

So, S ≥ 0

n/2[2a + (n - 1)d] ≥ 0

So, substituting the values of the variables into the equation, we have

n/2[2(-54) + (n - 1) × 1.5] ≥ 0

n/2[-108 + 1.5n - 1.5] ≥ 0

n/2[1.5n - 109.5] ≥ 0

n[1.5n - 109.5] ≥ 0

So, n ≥ 0 or 1.5n - 109.5 ≥ 0

n ≥ 0 or 1.5n ≥ 109.5

n ≥ 0 or n ≥ 109.5/1.5

n ≥ 0 or n ≥ 73

Since n > 0, the minimum value of n is 73.

So, the smallest number of terms of the AP that will make the sum of terms positive is 73.

Learn more about sum of terms of an AP here:

https://brainly.com/question/24579279

#SPJ1

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.