Advertisements
Advertisements
प्रश्न
If the first term of the G.P. is 16 and its sum to infinity is `96/17` find the common ratio.
Advertisements
उत्तर
Given:
First term, a = 16
Sum to infinity, S∞ = `96/17`
Formula for sum to infinity of a G.P.:
`S_∞ = a/(1-r)`, where ∣r∣ < 1
`96/17 = 16/(1-r)`
96(1 − r) = 17 × 16
96 − 96r = 272
−96r = 272 − 96
−96r = 176
`r = -176/96`
`= -11/6`
APPEARS IN
संबंधित प्रश्न
Evaluate `sum_(k=1)^11 (2+3^k )`
Find the sum to n terms of the sequence, 8, 88, 888, 8888… .
The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio `(3 + 2sqrt2) ":" (3 - 2sqrt2)`.
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.
Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn
If a, b, c are in A.P,; b, c, d are in G.P and ` 1/c, 1/d,1/e` are in A.P. prove that a, c, e are in G.P.
The seventh term of a G.P. is 8 times the fourth term and 5th term is 48. Find the G.P.
If 5th, 8th and 11th terms of a G.P. are p. q and s respectively, prove that q2 = ps.
Find three numbers in G.P. whose sum is 38 and their product is 1728.
Find three numbers in G.P. whose product is 729 and the sum of their products in pairs is 819.
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 \[39 + 13\sqrt{3}\] ?
The ratio of the sum of the first three terms to that of the first 6 terms of a G.P. is 125 : 152. Find the common ratio.
If S1, S2, ..., Sn are the sums of n terms of n G.P.'s whose first term is 1 in each and common ratios are 1, 2, 3, ..., n respectively, then prove that S1 + S2 + 2S3 + 3S4 + ... (n − 1) Sn = 1n + 2n + 3n + ... + nn.
Find the sum of the following serie to infinity:
`2/5 + 3/5^2 +2/5^3 + 3/5^4 + ... ∞.`
Find the sum of the following series to infinity:
10 − 9 + 8.1 − 7.29 + ... ∞
One side of an equilateral triangle is 18 cm. The mid-points of its sides are joined to form another triangle whose mid-points, in turn, are joined to form still another triangle. The process is continued indefinitely. Find the sum of the (i) perimeters of all the triangles. (ii) areas of all triangles.
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:
\[\frac{(a + b + c )^2}{a^2 + b^2 + c^2} = \frac{a + b + c}{a - b + c}\]
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.
Write the product of n geometric means between two numbers a and b.
Mark the correct alternative in the following question:
Let S be the sum, P be the product and R be the sum of the reciprocals of 3 terms of a G.P. Then p2R3 : S3 is equal to
For the G.P. if a = `7/243`, r = 3 find t6.
Find four numbers in G.P. such that sum of the middle two numbers is `10/3` and their product is 1
For the following G.P.s, find Sn.
p, q, `"q"^2/"p", "q"^3/"p"^2,` ...
For a G.P. a = 2, r = `-2/3`, find S6
For a G.P. sum of first 3 terms is 125 and sum of next 3 terms is 27, find the value of r
For a sequence, if Sn = 2(3n –1), find the nth term, hence show that the sequence is a G.P.
Find : `sum_("r" = 1)^oo (-1/3)^"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
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 three numbers in G.P. such that their sum is 35 and their product is 1000
Answer the following:
Find k so that k – 1, k, k + 2 are consecutive terms of a G.P.
Answer the following:
If for a G.P. first term is (27)2 and seventh term is (8)2, find S8
Answer the following:
If p, q, r, s are in G.P., show that (pn + qn), (qn + rn) , (rn + sn) are also in G.P.
If the pth and qth terms of a G.P. are q and p respectively, show that its (p + q)th term is `(q^p/p^q)^(1/(p - q))`
For a, b, c to be in G.P. the value of `(a - b)/(b - c)` 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 ______.
If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
