Advertisements
Advertisements
प्रश्न
Which term of the progression 0.004, 0.02, 0.1, ... is 12.5?
Advertisements
उत्तर
We have,
\[\frac{a_2}{a_1} = \frac{0 . 02}{0 . 004} = 5, \frac{a_3}{a_2} = \frac{0 . 1}{0 . 02} = 5\]
\[ \Rightarrow \frac{a_2}{a_1} = \frac{a_3}{a_2} = 5\]
\[\text { The given progression is a G . P . whose first term, a is 0 . 004 and common ratio, r is 5 }. \]
\[\text { Let the nth term be } 12 . 5 . \]
\[ \therefore a_n = 12 . 5\]
\[ \Rightarrow a r^{n - 1} = 12 . 5\]
\[ \Rightarrow (0 . 004)(5 )^{n - 1} = 12 . 5\]
\[ \Rightarrow (5 )^{n - 1} = \frac{12 . 5}{0 . 004}\]
\[ \Rightarrow (5 )^{n - 1} = 3125\]
\[ \Rightarrow (5 )^{n - 1} = (5 )^5 \]
\[\text { Comparing the power of both the sides }\]
\[ \Rightarrow n - 1 = 5\]
\[ \Rightarrow n = 6\]
\[\text { Thus, 6th term of the given G . P . is } 12 . 5\]
APPEARS IN
संबंधित प्रश्न
Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015,…
Find the sum to indicated number of terms in the geometric progressions x3, x5, x7, ... n terms (if x ≠ ± 1).
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)th to (2n)th term is `1/r^n`.
Find :
nth term of the G.P.
\[\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3\sqrt{3}}, . . .\]
Which term of the G.P.: `sqrt3, 3, 3sqrt3`, ... is 729?
If 5th, 8th and 11th terms of a G.P. are p. q and s respectively, prove that q2 = ps.
If the pth and qth terms of a G.P. are q and p, respectively, then show that (p + q)th term is \[\left( \frac{q^p}{p^q} \right)^\frac{1}{p - q}\].
Find the sum of the following geometric progression:
1, −1/2, 1/4, −1/8, ... to 9 terms;
Find the sum of the following geometric series:
1, −a, a2, −a3, ....to n terms (a ≠ 1)
Find the sum :
\[\sum^{10}_{n = 1} \left[ \left( \frac{1}{2} \right)^{n - 1} + \left( \frac{1}{5} \right)^{n + 1} \right] .\]
Find the sum of the following serie to infinity:
`2/5 + 3/5^2 +2/5^3 + 3/5^4 + ... ∞.`
If a, b, c are in G.P., prove that the following is also in G.P.:
a2, b2, c2
If xa = xb/2 zb/2 = zc, then prove that \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
The fractional value of 2.357 is
If a, b, c are in G.P. and x, y are AM's between a, b and b,c respectively, then
If x = (43) (46) (46) (49) .... (43x) = (0.0625)−54, the value of x is
In a G.P. if the (m + n)th term is p and (m − n)th term is q, then its mth term is
Check whether the following sequence is G.P. If so, write tn.
3, 4, 5, 6, …
Check whether the following sequence is G.P. If so, write tn.
7, 14, 21, 28, …
For the G.P. if a = `7/243`, r = 3 find t6.
Which term of the G.P. 5, 25, 125, 625, … is 510?
If for a sequence, tn = `(5^("n"-3))/(2^("n"-3))`, show that the sequence is a G.P. Find its first term and the common ratio
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.
The numbers x − 6, 2x and x2 are in G.P. Find 1st term
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
`1/5, (-2)/5, 4/5, (-8)/5, 16/5, ...`
Determine whether the sum to infinity of the following G.P.s exist, if exists find them:
9, 8.1, 7.29, ...
Express the following recurring decimal as a rational number:
`2.bar(4)`
If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term
Select the correct answer from the given alternative.
The common ratio for the G.P. 0.12, 0.24, 0.48, is –
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 -
The sum of 3 terms of a G.P. is `21/4` and their product is 1 then the common ratio is ______.
Answer the following:
In a G.P., the fourth term is 48 and the eighth term is 768. Find the tenth term
Answer the following:
Find `sum_("r" = 1)^"n" (2/3)^"r"`
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
If a, b, c, d are in G.P., prove that a2 – b2, b2 – c2, c2 – d2 are also in G.P.
If the expansion in powers of x of the function `1/((1 - ax)(1 - bx))` is a0 + a1x + a2x2 + a3x3 ....... then an is ______.
