document.write( "Question 1187229: 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. \n" ); document.write( "

Algebra.Com's Answer #818324 by KMST(5328) $\"\"$ $\"About$

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The sum of n terms of a geometric progression with first term 𝑎 and common ratio 𝑟
\n" ); document.write( "is $\"a%281-r%5En%29%2F%281-r%29\"$ .
\n" ); document.write( "If $\"r%3C1\"$ the sum to infinity is $\"a%2F%281-r%29\"$ .
\n" ); document.write( "From the information given in this problem we write two equations:
\n" ); document.write( " $\"a%281-r%5E3%29%2F%281-r%29=62\"$
\n" ); document.write( " $\"a%2F%281-r%29=62.5\"$
\n" ); document.write( "Dividing the first equation by the second one we get
\n" ); document.write( " $\"1-r%5E3=62%2F62.5\"$ --> $\"1-r%5E3=0.992\"$ --> $\"r%5E3=1-0.992\"$ --> $\"r%5E3=0.008\"$ --> $\"highlight%28r=0.2%29\"$
\n" ); document.write( "Substituting that value in $\"a%2F%281-r%29=62.5\"$ , we get
\n" ); document.write( " $\"a%2F%281-0.2%29=62.5\"$ --> $\"a%2F0.8=62.5\"$ --> $\"a=0.8%2A62.5\"$ --> $\"highlight%28a=50%29\"$ \n" ); document.write( "

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