Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. 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