Advertisements
Advertisements
प्रश्न
Find the sum to n terms of the sequence.
0.5, 0.05, 0.005, ...
Advertisements
उत्तर
Here, t1 = 0.5, t2 = 0.05, t3 = 0.005
∴ `"t"_2/"t"_1 = 0.05/0.5` = 0.1 and `"t"_3/"t"_2 = 0.005/0.05` = 0.1
∴ The given sequence is a G.P.
∴ a = 0.5 and r = 0.1
∴ Sn = `("a"(1 - "r"^"n"))/(1 - "r")`, for r < 1
= `(0.5[1 - (0.1)^"n"])/(1 - 0.1)`
= `0.5/0.9 [1 - (0.1)^"n"]`
= `5/9[1 - (1/10)^"n"]`
APPEARS IN
संबंधित प्रश्न
Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7thterm.
Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015,…
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
If a, b, c, d are in G.P, prove that (an + bn), (bn + cn), (cn + dn) are in G.P.
Find :
the 12th term of the G.P.
\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]
Find :
the 10th term of the G.P.
\[\sqrt{2}, \frac{1}{\sqrt{2}}, \frac{1}{2\sqrt{2}}, . . .\]
Which term of the G.P. :
\[\frac{1}{3}, \frac{1}{9}, \frac{1}{27} . . \text { . is } \frac{1}{19683} ?\]
Which term of the progression 18, −12, 8, ... is \[\frac{512}{729}\] ?
In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.
If \[\frac{a + bx}{a - bx} = \frac{b + cx}{b - cx} = \frac{c + dx}{c - dx}\] (x ≠ 0), then show that a, b, c and d are in G.P.
Find three numbers in G.P. whose sum is 65 and whose product is 3375.
The sum of first three terms of a G.P. is \[\frac{39}{10}\] and their product is 1. Find the common ratio and the terms.
Find the sum of the following geometric progression:
1, 3, 9, 27, ... to 8 terms;
Find the sum of the following series:
7 + 77 + 777 + ... to n terms;
How many terms of the series 2 + 6 + 18 + ... must be taken to make the sum equal to 728?
If a and b are the roots of x2 − 3x + p = 0 and c, d are the roots x2 − 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q − p) = 17 : 15.
How many terms of the G.P. `3, 3/2, 3/4` ..... are needed to give the sum `3069/512`?
A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.
One side of an equilateral triangle is 18 cm. The mid-points of its sides are joined to form another triangle whose mid-points, in turn, are joined to form still another triangle. The process is continued indefinitely. Find the sum of the (i) perimeters of all the triangles. (ii) areas of all triangles.
The sum of first two terms of an infinite G.P. is 5 and each term is three times the sum of the succeeding terms. Find the G.P.
The sum of three numbers which are consecutive terms of an A.P. is 21. If the second number is reduced by 1 and the third is increased by 1, we obtain three consecutive terms of a G.P. Find the numbers.
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an A.P. Find the numbers.
If a, b, c are in G.P., prove that:
\[\frac{1}{a^2 - b^2} + \frac{1}{b^2} = \frac{1}{b^2 - c^2}\]
If a, b, c are in G.P., prove that the following is also in G.P.:
a2, b2, c2
If a, b, c, d are in G.P., prove that:
(a2 + b2 + c2), (ab + bc + cd), (b2 + c2 + d2) are in G.P.
The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio `(3+2sqrt2):(3-2sqrt2)`.
If the fifth term of a G.P. is 2, then write the product of its 9 terms.
If logxa, ax/2 and logb x are in G.P., then write the value of x.
Let x be the A.M. and y, z be two G.M.s between two positive numbers. Then, \[\frac{y^3 + z^3}{xyz}\] is equal to
Check whether the following sequence is G.P. If so, write tn.
2, 6, 18, 54, …
Check whether the following sequence is G.P. If so, write tn.
1, –5, 25, –125 …
For the G.P. if r = `1/3`, a = 9 find t7
The value of a house appreciates 5% per year. How much is the house worth after 6 years if its current worth is ₹ 15 Lac. [Given: (1.05)5 = 1.28, (1.05)6 = 1.34]
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
`1/2, 1/4, 1/8, 1/16,...`
If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term
The midpoints of the sides of a square of side 1 are joined to form a new square. This procedure is repeated indefinitely. Find the sum of the areas of all the squares
Select the correct answer from the given alternative.
If common ratio of the G.P is 5, 5th term is 1875, the first term is -
Answer the following:
In a G.P., the fourth term is 48 and the eighth term is 768. Find the tenth term
