Sum to finite terms - Basic

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-one number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3.

Q1.  If the sum of an infinite G.P. be 9 and the sum of first two terms be 5, then the common ratio is

•   3/2
•  3
•  1/3
•   2/3

2/3

Q2.  2.357 =

•  2355/1000
•  2355/997
•  2355/999
•  None of these

2355/999

Q3.  The first term of a G.P. whose second term is 2 and sum to infinity is 8, will be

•   8
•  6
•  4
•   1

4

Q4.  The sum can be found of a infinite G.P. whose common ratio is r

•   For all values of r
•   For only positive value of r
•  Only for 0 < r < 1
•  Only for – 1 < r < 1(r is not euql to 0)

Only for – 1 < r < 1(r is not euql to 0)

Q5.  ]The sum of infinity of a geometric progression is 4/3 and the first term is 3/4 The common ratio is

•  7/16
•  7/8
•  1/16
•  9/16

7/16

Q6.  0.14189189189…. can be expressed as a rational number

•  21/48
•   7/148
•  7/256
•  21/148

21/148

Q7.  Sum of infinite number of terms in G.P. is 20 and sum of their square is 100. The common ratio of G.P. is

•   5
•  3/5
•  8/5
•  2/5

3/5

Q8.  If in an infinite G.P. first term is equal to the twice of the sum of the remaining terms, then its common ratio is

•  2
•   1
•   1/3
•   -1/3

1/3

Q9.  If x > 0, then the sum of the series e-x-e-2x+e-3x+....... is

•  1/(1+e-x)
•   1/(1-ex)
•   1/(1-e-x)
•  1/(1+ex)

1/(1+ex)

Q10.  The sum of the series 0.4 + 0.004 + 0.00004 + ..... is

•   11/25
•   4/9
•   40/99
•   None of the above

40/99

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