Advertisements
Advertisements
प्रश्न
Which term of the G.P. :
\[2, 2\sqrt{2}, 4, . . .\text { is }128 ?\]
उत्तर
\[\text { Here, first term, } a = 2 \]
\[\text { and common ratio }, r = \sqrt{2}\]
\[\text { Let the } n^{th} \text { term be } 128 . \]
\[ \therefore a_{n =} 128\]
\[ \Rightarrow a r^{n - 1} = 128\]
\[ \Rightarrow \left( 2 \right) \left( \sqrt{2} \right)^{n - 1} = 128\]
\[ \Rightarrow 2 (\sqrt{2} )^{n - 1} = 128\]
\[ \Rightarrow \left( \sqrt{2} \right)^{n - 1} = 64\]
\[ \Rightarrow \left( \sqrt{2} \right)^{n - 1} = \left( \sqrt{2} \right)^{12} \]
\[ \Rightarrow n - 1 = 12 \]
\[ \Rightarrow n = 13\]
\[\text { Thus, the } {13}^{th} \text { term of the given G . P . is } 128 .\]
APPEARS IN
संबंधित प्रश्न
Show that one of the following progression is a G.P. Also, find the common ratio in case:
4, −2, 1, −1/2, ...
Find:
the 10th term of the G.P.
\[- \frac{3}{4}, \frac{1}{2}, - \frac{1}{3}, \frac{2}{9}, . . .\]
Which term of the G.P. :
\[\sqrt{3}, 3, 3\sqrt{3}, . . . \text { is } 729 ?\]
Find three numbers in G.P. whose sum is 38 and their product is 1728.
Find the sum of the following geometric series:
x3, x5, x7, ... to n terms
Find the sum of the following series:
9 + 99 + 999 + ... to n terms;
How many terms of the G.P. 3, 3/2, 3/4, ... be taken together to make \[\frac{3069}{512}\] ?
The common ratio of a G.P. is 3 and the last term is 486. If the sum of these terms be 728, find the first term.
The fifth term of a G.P. is 81 whereas its second term is 24. Find the series and sum of its first eight terms.
Find the sum of 2n terms of the series whose every even term is 'a' times the term before it and every odd term is 'c' times the term before it, the first term being unity.
Find the sum of the following serie to infinity:
\[1 - \frac{1}{3} + \frac{1}{3^2} - \frac{1}{3^3} + \frac{1}{3^4} + . . . \infty\]
Find the rational numbers having the following decimal expansion:
\[3 . 5\overline 2\]
Show that in an infinite G.P. with common ratio r (|r| < 1), each term bears a constant ratio to the sum of all terms that follow it.
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.
If a, b, c are in A.P., b,c,d are in G.P. and \[\frac{1}{c}, \frac{1}{d}, \frac{1}{e}\] are in A.P., prove that a, c,e are in G.P.
If p, q be two A.M.'s and G be one G.M. between two numbers, then G2 =
Check whether the following sequence is G.P. If so, write tn.
1, –5, 25, –125 …
For the G.P. if a = `7/243`, r = 3 find t6.
For the G.P. if r = − 3 and t6 = 1701, find a.
Find three numbers in G.P. such that their sum is 21 and sum of their squares is 189.
A ball is dropped from a height of 80 ft. The ball is such that it rebounds `(3/4)^"th"` of the height it has fallen. How high does the ball rebound on 6th bounce? How high does the ball rebound on nth bounce?
The numbers 3, x, and x + 6 form are in G.P. Find nth term
Find the sum to n terms of the sequence.
0.2, 0.02, 0.002, ...
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]
Express the following recurring decimal as a rational number:
`2.3bar(5)`
If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term
If the first term of the G.P. is 6 and its sum to infinity is `96/17` find the common ratio.
Find : `sum_("r" = 1)^oo (-1/3)^"r"`
Find `sum_("r" = 0)^oo (-8)(-1/2)^"r"`
A ball is dropped from a height of 10m. It bounces to a height of 6m, then 3.6m and so on. Find the total distance travelled by the ball
Insert two numbers between 1 and −27 so that the resulting sequence is a G.P.
If a, b, c, d are four distinct positive quantities in G.P., then show that a + d > b + c
In a G.P. of positive terms, if any term is equal to the sum of the next two terms. Then the common ratio of the G.P. 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.
Let `{a_n}_(n = 0)^∞` be a sequence such that a0 = a1 = 0 and an+2 = 2an+1 – an + 1 for all n ≥ 0. Then, `sum_(n = 2)^∞ a^n/7^n` is equal to ______.
The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in ______.
The sum of infinite number of terms of a decreasing G.P. is 4 and the sum of the terms to m squares of its terms to infinity is `16/3`, then the G.P. is ______.
If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
