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CA Foundation Exam  >  CA Foundation Tests  >  Quantitative Aptitude for CA Foundation  >  Test: Arithmetic And Geometric Progressions - 4 - CA Foundation MCQ

Test: Arithmetic And Geometric Progressions - 4 - CA Foundation MCQ


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30 Questions MCQ Test Quantitative Aptitude for CA Foundation - Test: Arithmetic And Geometric Progressions - 4

Test: Arithmetic And Geometric Progressions - 4 for CA Foundation 2024 is part of Quantitative Aptitude for CA Foundation preparation. The Test: Arithmetic And Geometric Progressions - 4 questions and answers have been prepared according to the CA Foundation exam syllabus.The Test: Arithmetic And Geometric Progressions - 4 MCQs are made for CA Foundation 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Arithmetic And Geometric Progressions - 4 below.
Solutions of Test: Arithmetic And Geometric Progressions - 4 questions in English are available as part of our Quantitative Aptitude for CA Foundation for CA Foundation & Test: Arithmetic And Geometric Progressions - 4 solutions in Hindi for Quantitative Aptitude for CA Foundation course. Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free. Attempt Test: Arithmetic And Geometric Progressions - 4 | 40 questions in 40 minutes | Mock test for CA Foundation preparation | Free important questions MCQ to study Quantitative Aptitude for CA Foundation for CA Foundation Exam | Download free PDF with solutions
Test: Arithmetic And Geometric Progressions - 4 - Question 1
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 In a G.P. if the (p+q)th term is m and the (p-q)th term is n then the pth term is _________.

Test: Arithmetic And Geometric Progressions - 4 - Question 2
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The sum of n terms of the series 0.5+0.05+0.555+………… is

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Test: Arithmetic And Geometric Progressions - 4 - Question 3
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 If a, b-a, c-a are in G.P. and a=b/3=c/5 then a, b, c are in

Test: Arithmetic And Geometric Progressions - 4 - Question 4
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The sum of term of the series 5+55+555+…..is
Test: Arithmetic And Geometric Progressions - 4 - Question 5
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If a, b, (c+1) are in G.P. and a=(b-c)2 then a, b, c are in
Test: Arithmetic And Geometric Progressions - 4 - Question 6
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 If S1, S2, S3, ………Sn are the sums of infinite G.P.s whose first terms are 1, 2, 3……n and whose common ratios are 1/2, 1/3, ……1/(n+1) then the value of S1+S2+S3+ ……Sn is
Test: Arithmetic And Geometric Progressions - 4 - Question 7
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If a, b, c are in G.P. then the value of (a-b+c)(a+b+c)2-(a+b+c)(a2+b2+c2) is given by
Test: Arithmetic And Geometric Progressions - 4 - Question 8
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If a1/x=b1/y=c1/z and a, b, c are in G.P. then x, y, z are in
Test: Arithmetic And Geometric Progressions - 4 - Question 9
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 If a, b, (c+1) are in G.P. and a=(b-c)2 then a, b, c are in
Test: Arithmetic And Geometric Progressions - 4 - Question 10
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 If a, b, c are in G.P. then a2+b2, ab+bc, b2+c2 are in
Test: Arithmetic And Geometric Progressions - 4 - Question 11
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 If a, b, c are in G.P then the value of a (b2+c2)-c(a2+b2) is given by
Test: Arithmetic And Geometric Progressions - 4 - Question 12
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If a, b, c are in G.P. then value of a2b2c2(a-3+b-3+c-3)-(a3+b3+c3) is given by
Test: Arithmetic And Geometric Progressions - 4 - Question 13
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 If a, b, c, d are in G.P. then a+b, b+c, c+d are in
Test: Arithmetic And Geometric Progressions - 4 - Question 14
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 If a, b, c are in A.P. a, x, b are in G.P. and b, y, c are in G.P. then x2, b2, y2 are in
Test: Arithmetic And Geometric Progressions - 4 - Question 15
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If a, b, c, d are in G.P. then the value of (b-c)2+(c-a)2+(d-b)2-(a-d)2 is given by
Test: Arithmetic And Geometric Progressions - 4 - Question 16
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 If (a-b), (b-c), (c-a) are in G.P. then the value of (a+b+c)2-3(ab+bc+ca) is given by
Test: Arithmetic And Geometric Progressions - 4 - Question 17
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If a, b, c, d are in G.P. then (a-b)2, (b-c)2,(c-a)2 are in
Test: Arithmetic And Geometric Progressions - 4 - Question 18
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 If a, b, x, y, z are positive numbers such that a, x, b are in A.P. and a, y, b are in G.P. and z=(2ab)/(a+b)then
Test: Arithmetic And Geometric Progressions - 4 - Question 19
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If a, b-a, c-a are in G.P. and a=b/3=c/5 then a, b, c are in
Test: Arithmetic And Geometric Progressions - 4 - Question 20
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 If a, b, c, d are in G.P. then the value of b(ab-cd)-(c+a)(b2-c2) is ________
Test: Arithmetic And Geometric Progressions - 4 - Question 21
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The least value of n for which the sum of n terms of the series 1+3+32+………..is greater than 7000 is _________.
Test: Arithmetic And Geometric Progressions - 4 - Question 22
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If a, b, c are in A.P. and x, y, z in G.P. then the value of (xb.yc.za) ÷ (xc.ya.zb) is _________.
Test: Arithmetic And Geometric Progressions - 4 - Question 23
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If a, b, c are the pth, qth and rth terms of a G.P. respectively the value of aq-r. br-p. cp-q is ___________.
Test: Arithmetic And Geometric Progressions - 4 - Question 24
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If a, b, c are in G.P. then the value of a(b2+c2)-c(a2+b2) is __________
Test: Arithmetic And Geometric Progressions - 4 - Question 25
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If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Sn and R-n.
Test: Arithmetic And Geometric Progressions - 4 - Question 26
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If the sum of three numbers in G.P. is 21 and the sum of their squares is 189 the numbers are __________.
Test: Arithmetic And Geometric Progressions - 4 - Question 27
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The sum of n terms of the series 7+77+777+……is
Test: Arithmetic And Geometric Progressions - 4 - Question 28
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If a, b, c, d are in G.P. then the value of (ab+bc+cd)2-(a2+b2+c2)(b2+c2+d2)is ______.
Test: Arithmetic And Geometric Progressions - 4 - Question 29
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If 1+a+a2+………∞=x and 1+b+b2+……∞=y then 1+ab+a2b2+………∞ = x is given by ________.
Detailed Solution for Test: Arithmetic And Geometric Progressions - 4 - Question 29

ANSWER :- a

Solution :- Given, x=1+a+a^2+......∞

Since this is a infinite G.P. series, where, (first term)=1 and (common difference)=a,

So, x = 1/(1−a)

⇒ x−ax=1

⇒ ax=x−1

⇒ a=(x−1)/x

Similarly, y=1+b+b^2 +......∞ is a infinite G.P. series, where, (first term)=1 and

 (common difference)=b,

So, y = 1/(1−b)

⇒ y−by=1

⇒ by=y−1

⇒ b=(y−1)/y

And now,

L.H.S.=1 + ab + a^2b^2 + ....∞

= 1/(1−ab) (infinte G.P. series where (first term)=1 and (common difference)=ab

= 1/{1−(x−1/x)(y−1/y)}

           = xy/(xy−xy+x+y−1)

= (xy)/(x+y−1)

Test: Arithmetic And Geometric Progressions - 4 - Question 30
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Sum upto ∞ of the series 1/2+1/32+1/23+1/34+1/25+1/36+……is
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