adhikaribhaskar70
Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

a) If the 5th term of an A.P. is double the 7th term, show that the sum of the 17 terms zero.​

Sagot :

Answer:

see explanation

Step-by-step explanation:

The nth term of an AP is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₅ is double a₇ , then

a₁ + 4d = 2(a₁ + 6d) , that is

a₁ + 4d = 2a₁ + 12d ( subtract a₁ from both sides )

4d = a₁ + 12d ( subtract 12d from both sides )

- 8d = a₁

The sum of n terms of an AP is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ] , substitute values

[tex]S_{17}[/tex] = [tex]\frac{17}{2}[/tex] ( 2(- 8d) + 16d)

     = 8.5(- 16d + 16d)

     = 8.5 × 0

     = 0

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