Advertisements
Advertisements
प्रश्न
For the G.P. if a = `2/3`, t6 = 162, find r.
Advertisements
उत्तर
Given, a = `2/3`, t6 = 162
tn = arn–1
∴ t6 = `(2/3)("r"^(6 - 1))`
∴ 162 = `2/3"r"^5`
∴ r5 = `162 xx 3/2`
∴ r5 = 35
∴ r = 3
APPEARS IN
संबंधित प्रश्न
Find the 20th and nthterms of the G.P. `5/2, 5/4 , 5/8,...`
Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).
Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
Find:
the ninth term of the G.P. 1, 4, 16, 64, ...
Find:
the 10th term of the G.P.
\[- \frac{3}{4}, \frac{1}{2}, - \frac{1}{3}, \frac{2}{9}, . . .\]
Which term of the progression 0.004, 0.02, 0.1, ... is 12.5?
The sum of three numbers in G.P. is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting numbers 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.
Find the sum of the following geometric progression:
(a2 − b2), (a − b), \[\left( \frac{a - b}{a + b} \right)\] to n terms;
The sum of n terms of the G.P. 3, 6, 12, ... is 381. Find the value of n.
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.
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 \[\frac{1}{r^n}\].
Find the sum of the following serie to infinity:
`2/5 + 3/5^2 +2/5^3 + 3/5^4 + ... ∞.`
Find the rational numbers having the following decimal expansion:
\[0 . 6\overline8\]
Find k such that k + 9, k − 6 and 4 form three consecutive terms of a G.P.
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an A.P. Find the numbers.
If a, b, c, d are in G.P., prove that:
(b + c) (b + d) = (c + a) (c + d)
If pth, qth, rth and sth terms of an A.P. be in G.P., then prove that p − q, q − r, r − s 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.
Find the geometric means of the following pairs of number:
−8 and −2
If logxa, ax/2 and logb x are in G.P., then write the value of x.
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 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
If the sum of first two terms of an infinite GP is 1 every term is twice the sum of all the successive terms, then its first term is
If p, q, r, s are in G.P. show that p + q, q + r, r + s are also in G.P.
The numbers x − 6, 2x and x2 are in G.P. Find x
Find: `sum_("r" = 1)^10 5 xx 3^"r"`
If one invests Rs. 10,000 in a bank at a rate of interest 8% per annum, how long does it take to double the money by compound interest? [(1.08)5 = 1.47]
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 areas of all the squares
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.
If for a G.P. `"t"_6/"t"_3 = 1458/54` then r = ?
Select the correct answer from the given alternative.
Which of the following is not true, where A, G, H are the AM, GM, HM of a and b respectively. (a, b > 0)
Answer the following:
Find three numbers in G.P. such that their sum is 35 and their product is 1000
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 ______.
In a G.P. of even number of terms, the sum of all terms is 5 times the sum of the odd terms. The common ratio of the G.P. is ______.
The third term of G.P. is 4. The product of its first 5 terms is ______.
For a, b, c to be in G.P. the value of `(a - b)/(b - c)` is equal to ______.
