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# Notes | EduRev

## JEE Revision Notes

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## JEE : Notes | EduRev

The document Notes | EduRev is a part of the JEE Course JEE Revision Notes.
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• If â€˜aâ€™ is the first term and â€˜râ€™ is the common ratio of the geometric progression, then its nth term is given by an = arn-1
• The sum, Sn of the first â€˜nâ€™ terms of the G.P. is given by Sn = a (rn â€“ 1)/ (r-1), when r â‰ 1; = na , if r =1
• If -1 < x < 1, then limxn = 0, as n â†’âˆž. Hence, the sum of an infinite G.P. is 1+x+x2+ â€¦.. = 1/(1-x)
• If -1 < r< 1, then the sum of the infinite G.P. is a +ar+ ar2+ â€¦.. = a/(1-r)
• If each term of the G.P is multiplied or divided by a non-zero fixed constant, the resulting sequence is again a G.P.
• If a1, a2, a3, â€¦. and b1, b2, b3, â€¦ are two geometric progressions, then a1b1, a2b2, a3b3, â€¦â€¦ is also a geometric progression and a1/b1, a2/b2, ... ... ..., an/bwill also be in G.P.
• Suppose a1, a2, a3, â€¦â€¦,an are in G.P. then an, anâ€“1, anâ€“2, â€¦â€¦, a3, a2, a1 will also be in G.P.
• Taking the inverse of a G.P. also results a G.P. Suppose a1, a2, a3, â€¦â€¦,an are in G.P then 1/a1, 1/a2, 1/a3 â€¦â€¦, 1/an will also be in G.P
• If we need to assume three numbers in G.P. then they should be assumed as   a/b, a, ab  (here common ratio is b)
• Four numbers in G.P. should be assumed as a/b3, a/b, ab, ab3 (here common ratio is b2)
• Five numbers in G.P. a/b2, a/b, a, ab, ab2  (here common ratio is b)
• If a1, a2, a3,â€¦ ,an is a G.P (ai> 0 âˆ€i), then log a1, log a2, log a3, â€¦â€¦, log an is an A.P. In this case, the converse of the statement also holds good.
• If three terms are in G.P., then the middle term is called the geometric mean (G.M.) between the two. So if a, b, c are in G.P., then b = âˆšac is the geometric mean of a and c.
• Likewise, if a1, a2, â€¦â€¦,an are non-zero positive numbers, then their G.M.(G) is given by G = (a1a2a3 â€¦â€¦ an)1/n.
• If G1, G2, â€¦â€¦Gare n geometric means between and a and b then a, G1, G2, â€¦â€¦,Gn b will be a G.P.
• Here b = arn+1, â‡’ r = n+1âˆšb/a, Hence, G1 = a. n+1âˆšb/a, G= a(n+1âˆšb/a)2,â€¦, Gn = a(n+1âˆšb/a)n.
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