winniewin
Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Please help me with this question
The ratio of 7th term to the 9th term is 5:8. find the common difference

Sagot :

sqdancefan

9514 1404 393

Answer:

  -3/8 × (first term)

Step-by-step explanation:

The general term of an arithmetic sequence is ...

  an = a1 +d(n -1)

Then the ratio of interest is ...

  (7th term)/(9th term) = 5/8

  (a1 +6d)/(a1 +8d) = 5/8

Multiplying by 8(a1 +8d) we get ...

  8(a1 +6d) = 5(a1 +8d)

  8a1 +48d = 5a1 +40d . . . . . . eliminate parentheses

  8d = -3a1 . . . . . . . . . . . . . . subtract 40d+8a1

  d = (-3/8)a1 . . . . . . . . . . divide by 8 to find the common difference

The common difference is -3/8 times the first term.

__

Example

Let the first term be -16. Then the common difference is (-3/8)(-16) = 6. The first 9 terms of the sequence are ...

  -16, -10, -4, 2, 8, 14, 20, 26, 32

The ratio of the 7th and 9th terms is ...

  20/32 = 5/8 . . . . as required

__

In the general case, the ratio of terms would be ...

  (a1 +(-3/8a1)(7 -1))/(a1 +(-3/8a1)(9 -1)) = (1 -6(3/8))/(1 -8(3/8)) = (-10/8)/(-16/8) = 5/8

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.