Advertisements
Advertisements
प्रश्न
Find the sum to n terms of the sequence.
0.2, 0.02, 0.002, ...
Advertisements
उत्तर
Here, t1 = 0.2, t2 = 0.02, t3 = 0.002
∴ `"t"_2/"t"_1 = 0.02/0.2 = 0.1` and `"t"_3/"t"_2 = 0.002/0.02 = 0.1`
∴ The given sequence is a G.P.
∴ a = 0.2 and r = 0.1
∴ Sn = `("a"(1 - "r"^"n"))/(1 - "r")` for r < 1
= `(0.2[1 - (0.1)^"n"])/(1 - 0.1)`
`= 0.2/0.9 [1 - (0.1)^"n"]`
= `2/9[1 - (1/10)^"n"]`
APPEARS IN
संबंधित प्रश्न
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 n terms of the sequence, 8, 88, 888, 8888… .
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
Find :
the 8th term of the G.P. 0.3, 0.06, 0.012, ...
If the pth and qth terms of a G.P. are q and p, respectively, then show that (p + q)th term is \[\left( \frac{q^p}{p^q} \right)^\frac{1}{p - q}\].
The product of three numbers in G.P. is 216. If 2, 8, 6 be added to them, the results are in A.P. Find the numbers.
The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.
How many terms of the series 2 + 6 + 18 + ... must be taken to make the sum equal to 728?
The ratio of the sum of the first three terms to that of the first 6 terms of a G.P. is 125 : 152. Find the common ratio.
Find the rational numbers having the following decimal expansion:
\[0 . \overline3\]
The sum of three numbers a, b, c in A.P. is 18. If a and b are each increased by 4 and c is increased by 36, the new numbers form a G.P. Find a, b, c.
If a, b, c are in G.P., prove that the following is also in G.P.:
a2, b2, c2
If a, b, c are in G.P., then prove that:
If a, b, c are in A.P. and a, b, d are in G.P., then prove that a, a − b, d − c are in G.P.
Insert 5 geometric means between \[\frac{32}{9}\text{and}\frac{81}{2}\] .
If (p + q)th and (p − q)th terms of a G.P. are m and n respectively, then write is pth term.
If in an infinite G.P., first term is equal to 10 times the sum of all successive terms, then its common ratio is
If the first term of a G.P. a1, a2, a3, ... is unity such that 4 a2 + 5 a3 is least, then the common ratio of G.P. is
For the G.P. if r = − 3 and t6 = 1701, find a.
The numbers 3, x, and x + 6 form are in G.P. Find x
The numbers 3, x, and x + 6 form are in G.P. Find nth term
Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after 3 years.
For a G.P. sum of first 3 terms is 125 and sum of next 3 terms is 27, find the value of r
Find: `sum_("r" = 1)^10(3 xx 2^"r")`
Find : `sum_("r" = 1)^oo (-1/3)^"r"`
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 perimeters 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:
If pth, qth and rth terms of a G.P. are x, y, z respectively. Find the value of xq–r .yr–p .zp–q
Answer the following:
Which 2 terms are inserted between 5 and 40 so that the resulting sequence is G.P.
Answer the following:
If a, b, c are in G.P. and ax2 + 2bx + c = 0 and px2 + 2qx + r = 0 have common roots then verify that pb2 – 2qba + ra2 = 0
Answer the following:
Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`
If a, b, c, d are four distinct positive quantities in G.P., then show that a + d > b + c
The third term of G.P. is 4. The product of its first 5 terms is ______.
Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.
