SOLUTION: A geometric progression has first term 𝑎 and common ratio 𝑟. The sum of the first three terms is 62 and the sum to infinity is 62.5. Find the value of 𝑎 and the value of

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Question 1187234: A geometric progression has first term 𝑎 and common ratio 𝑟. The sum of the first three terms is 62 and the sum to infinity is 62.5. Find the value of 𝑎 and the value of 𝑟.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I answered this as Question 1187229
The sum of n terms of a geometric progression with first term 𝑎 and common ratio 𝑟
is a%281-r%5En%29%2F%281-r%29 .
If r%3C1 the sum to infinity is a%2F%281-r%29 .
From the information given in this problem we write two equations:
a%281-r%5E3%29%2F%281-r%29=62
a%2F%281-r%29=62.5
Dividing the first equation by the second one we get
1-r%5E3=62%2F62.5-->1-r%5E3=0.992-->r%5E3=1-0.992-->r%5E3=0.008-->highlight%28r=0.2%29
Substituting that value in a%2F%281-r%29=62.5 , we get
a%2F%281-0.2%29=62.5-->a%2F0.8=62.5-->a=0.8%2A62.5-->highlight%28a=50%29