Advertisements
Advertisements
प्रश्न
Given a G.P. with a = 729 and 7th term 64, determine S7.
Advertisements
उत्तर
गुणोत्तर श्रेणी का पहला पद, a = 729
मान लीजिए सार्व अनुपात = r
∴ 7वाँ पद = ar7-1 = ar6
729 r6 = 64
⇒ r6 = `64/729 = (2/3)^6`
∴ r = `2/3`
अब S7 = `("a"(1 - "r"^"n"))/(1 - "r")`
= `(729[1 - (2/3)^7])/(1 - 2/3)`
= `729 xx 3 xx [(2187 - 128)/2187]`
= `(729 xx 3)/2187 (2059)`
= 2059
APPEARS IN
संबंधित प्रश्न
Find the sum to indicated number of terms in the geometric progressions x3, x5, x7, ... n terms (if x ≠ ± 1).
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.
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 12th term of the G.P.
\[\frac{1}{a^3 x^3}, ax, a^5 x^5 , . . .\]
Which term of the progression 0.004, 0.02, 0.1, ... is 12.5?
If a, b, c, d and p are different real numbers such that:
(a2 + b2 + c2) p2 − 2 (ab + bc + cd) p + (b2 + c2 + d2) ≤ 0, then show that a, b, c and d are in G.P.
The sum of first three terms of a G.P. is 13/12 and their product is − 1. Find the G.P.
Find the sum of the following geometric series:
0.15 + 0.015 + 0.0015 + ... to 8 terms;
Find the sum of the following geometric series:
1, −a, a2, −a3, ....to n terms (a ≠ 1)
Find the sum of the following serie:
5 + 55 + 555 + ... to n terms;
How many terms of the sequence \[\sqrt{3}, 3, 3\sqrt{3},\] ... must be taken to make the sum \[39 + 13\sqrt{3}\] ?
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 \[\frac{1}{r^n}\].
A person has 2 parents, 4 grandparents, 8 great grandparents, and so on. Find the number of his ancestors during the ten generations preceding his own.
If S denotes the sum of an infinite G.P. S1 denotes the sum of the squares of its terms, then prove that the first term and common ratio are respectively
\[\frac{2S S_1}{S^2 + S_1}\text { and } \frac{S^2 - S_1}{S^2 + S_1}\]
If a, b, c are in G.P., prove that the following is also in G.P.:
a3, b3, c3
If pth, qth and rth terms of a G.P. re x, y, z respectively, then write the value of xq − r yr − pzp − q.
If a = 1 + b + b2 + b3 + ... to ∞, then write b in terms of a.
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 pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. 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
For the G.P. if r = `1/3`, a = 9 find t7
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
For the following G.P.s, find Sn
3, 6, 12, 24, ...
For a G.P. If t3 = 20 , t6 = 160 , find S7
For a sequence, if Sn = 2(3n –1), find the nth term, hence show that the sequence is a G.P.
If S, P, R are the sum, product, and sum of the reciprocals of n terms of a G.P. respectively, then verify that `["S"/"R"]^"n"` = P2
Find: `sum_("r" = 1)^10(3 xx 2^"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 common ratio of the G.P is 5, 5th term is 1875, the first term is -
Answer the following:
For a G.P. a = `4/3` and t7 = `243/1024`, find the value of r
Answer the following:
Find the nth term of the sequence 0.6, 0.66, 0.666, 0.6666, ...
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.
Answer the following:
Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`
If a, b, c, d are four distinct positive quantities in G.P., then show that a + d > b + c
For an increasing G.P. a1, a2 , a3 ........., an, if a6 = 4a4, a9 – a7 = 192, then the value of `sum_(i = 1)^∞ 1/a_i` is ______.
Let A1, A2, A3, .... be an increasing geometric progression of positive real numbers. If A1A3A5A7 = `1/1296` and A2 + A4 = `7/36`, then the value of A6 + A8 + A10 is equal to ______.
