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Question

# An infinite geometric progression a1, a2, a3, ..... has the property that an=3(an+1+an+2+......) for every n≥1. If the sum a1, a2, a3, .....=32, then a5 is

A

1/32

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B

2/32

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C

3/32

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D

4/32

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Solution

## The correct option is C 3/32 According to question, an=3(an+1+an+2+…) From the above equation we can conclude that every nth term is equal to three times the sum of all the terms after the nth term i.e. 1st term i.e. 1st term is equal to 3 times the sum of all terms starting from 2nd term and 2nd term is equal to three times the sum of all the terms starting from 3rd term. So, a1+a2+a3+a4+…=32⇒a1+(a1/3)=32⇒a1=24 Then, a2+a3+a4+a+5+…=32–24=8⇒a2+(a2/3)=8⇒a2=6 So, common ratio = a2/a1=6/24=14 Therefore, a5=ar5−1=ar4 = 24 x (14)4=332

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