Advertisements
Advertisements
प्रश्न
The third term of G.P. is 4. The product of its first 5 terms is ______.
विकल्प
43
44
45
None of these
Advertisements
उत्तर
The third term of G.P. is 4. The product of its first 5 terms is 45.
Explanation:
Given that T3 = 4
⇒ ar3–1 = 4
⇒ ar2 = 4
Product of first 5 terms = a · ar · ar2 · ar3 · ar4
= a5r10
= (ar2)5
= (4)5
APPEARS IN
संबंधित प्रश्न
Which term of the following sequence:
`2, 2sqrt2, 4,.... is 128`
if `(a+ bx)/(a - bx) = (b +cx)/(b - cx) = (c + dx)/(c- dx) (x != 0)` then show that a, b, c and d are in G.P.
Find:
the ninth term of the G.P. 1, 4, 16, 64, ...
Find :
the 12th term of the G.P.
\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]
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 125 and the sum of their products taken in pairs is \[87\frac{1}{2}\] . Find them.
The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.
Find the sum of the following geometric series:
\[\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . \text { to 5 terms };\]
Find the sum of the following geometric series:
1, −a, a2, −a3, ....to n terms (a ≠ 1)
How many terms of the sequence \[\sqrt{3}, 3, 3\sqrt{3},\] ... must be taken to make the sum \[39 + 13\sqrt{3}\] ?
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying the odd places. Find the common ratio of the G.P.
If a, b, c are in G.P., prove that:
\[\frac{(a + b + c )^2}{a^2 + b^2 + c^2} = \frac{a + b + c}{a - b + c}\]
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, d are in G.P., prove that:
(a2 + b2), (b2 + c2), (c2 + d2) are in G.P.
If \[\frac{1}{a + b}, \frac{1}{2b}, \frac{1}{b + c}\] are three consecutive terms of an A.P., prove that a, b, c are the three consecutive terms of a G.P.
If the sum of an infinite decreasing G.P. is 3 and the sum of the squares of its term is \[\frac{9}{2}\], then write its first term and common difference.
If S be the sum, P the product and R be the sum of the reciprocals of n terms of a GP, then P2 is equal to
The value of 91/3 . 91/9 . 91/27 ... upto inf, is
The sum of an infinite G.P. is 4 and the sum of the cubes of its terms is 92. The common ratio of the original G.P. is
If p, q be two A.M.'s and G be one G.M. between two numbers, then G2 =
If x = (43) (46) (46) (49) .... (43x) = (0.0625)−54, the value of x 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.
The numbers 3, x, and x + 6 form are in G.P. Find 20th term.
The numbers 3, x, and x + 6 form are in G.P. Find nth term
The numbers x − 6, 2x and x2 are in G.P. Find 1st term
For a G.P. a = 2, r = `-2/3`, find S6
For a G.P. if a = 2, r = 3, Sn = 242 find n
Find the sum to n terms of the sequence.
0.5, 0.05, 0.005, ...
Find the sum to n terms of the sequence.
0.2, 0.02, 0.002, ...
Express the following recurring decimal as a rational number:
`0.bar(7)`
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
Select the correct answer from the given alternative.
If for a G.P. `"t"_6/"t"_3 = 1458/54` then r = ?
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:
For a G.P. if t2 = 7, t4 = 1575 find a
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
Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.
The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in ______.
