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
Find the sum of the products of the corresponding terms of the sequences `2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2`
If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.
If a, b, c and d are in G.P. show that (a2 + b2 + c2) (b2 + c2 + d2) = (ab + bc + cd)2 .
Show that one of the following progression is a G.P. Also, find the common ratio in case:
−2/3, −6, −54, ...
Show that one of the following progression is a G.P. Also, find the common ratio in case:
\[a, \frac{3 a^2}{4}, \frac{9 a^3}{16}, . . .\]
If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.
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.
Find the sum of the following geometric series:
\[\sqrt{2} + \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} + . . .\text { to 8 terms };\]
Find the sum of the following series:
7 + 77 + 777 + ... to n terms;
How many terms of the G.P. `3, 3/2, 3/4` ..... are needed to give the sum `3069/512`?
Find the rational numbers having the following decimal expansion:
\[0 . 6\overline8\]
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.
If a, b, c are in G.P., prove that \[\frac{1}{\log_a m}, \frac{1}{\log_b m}, \frac{1}{\log_c m}\] are in A.P.
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., show that a, (a − b), (d − c) are in G.P.
Find the geometric means of the following pairs of number:
2 and 8
If (p + q)th and (p − q)th terms of a G.P. are m and n respectively, then write is pth term.
If pth, qth and rth terms of a G.P. re x, y, z respectively, then write the value of xq − r yr − pzp − q.
If x = (43) (46) (46) (49) .... (43x) = (0.0625)−54, the value of x is
The product (32), (32)1/6 (32)1/36 ... to ∞ is equal to
For the G.P. if a = `7/243`, r = 3 find t6.
Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third 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 10 years.
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 n years.
The numbers x − 6, 2x and x2 are in G.P. Find 1st term
For the following G.P.s, find Sn.
`sqrt(5)`, −5, `5sqrt(5)`, −25, ...
Find the sum to n terms of the sequence.
0.5, 0.05, 0.005, ...
Find: `sum_("r" = 1)^10(3 xx 2^"r")`
Express the following recurring decimal as a rational number:
`2.3bar(5)`
Find : `sum_("r" = 1)^oo 4(0.5)^"r"`
Find : `sum_("r" = 1)^oo (-1/3)^"r"`
Select the correct answer from the given alternative.
The tenth term of the geometric sequence `1/4, (-1)/2, 1, -2,` ... is –
Select the correct answer from the given alternative.
Which term of the geometric progression 1, 2, 4, 8, ... is 2048
Answer the following:
Find the sum of the first 5 terms of the G.P. whose first term is 1 and common ratio is `2/3`
Answer the following:
If p, q, r, s are in G.P., show that (p2 + q2 + r2) (q2 + r2 + s2) = (pq + qr + rs)2
If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.
The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in ______.
