Advertisements
Advertisements
प्रश्न
For the G.P. if r = − 3 and t6 = 1701, find a.
उत्तर
tn = arn−1, where r = − 3
∴ t6 = a(−3)6 −1 = 1701
∴ a(− 3)5 = 1701
∴ − 243a = 1701
∴ a = `(1701)/(-243)`
= − 7
APPEARS IN
संबंधित प्रश्न
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.
If a and b are the roots of are roots of x2 – 3x + p = 0 , and c, d are roots of x2 – 12x + q = 0, where a, b, c, d, form a G.P. Prove that (q + p): (q – p) = 17 : 15.
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 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.
Find the sum of the following geometric progression:
2, 6, 18, ... to 7 terms;
Find the sum of the following series:
0.5 + 0.55 + 0.555 + ... to n terms.
The sum of n terms of the G.P. 3, 6, 12, ... is 381. Find the value of n.
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 \[\frac{1}{r^n}\].
If a and b are the roots of x2 − 3x + p = 0 and c, d are the roots x2 − 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p) : (q − p) = 17 : 15.
Find the sum of the terms of an infinite decreasing G.P. in which all the terms are positive, the first term is 4, and the difference between the third and fifth term is equal to 32/81.
Find the rational number whose decimal expansion is \[0 . 423\].
Find the rational numbers having the following decimal expansion:
\[0 .\overline {231 }\]
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 are in G.P., prove that the following is also in G.P.:
a2 + b2, ab + bc, b2 + c2
If A1, A2 be two AM's and G1, G2 be two GM's between a and b, then find the value of \[\frac{A_1 + A_2}{G_1 G_2}\]
Write the product of n geometric means between two numbers a and b.
If a = 1 + b + b2 + b3 + ... to ∞, then write b in terms of a.
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 r = `1/3`, a = 9 find t7
For the G.P. if a = `2/3`, t6 = 162, find r.
Which term of the G.P. 5, 25, 125, 625, … is 510?
Find five numbers in G.P. such that their product is 1024 and fifth term is square of the third term.
The numbers 3, x, and x + 6 form are in G.P. Find 20th term.
Mosquitoes are growing at a rate of 10% a year. If there were 200 mosquitoes in the beginning. Write down the number of mosquitoes after 3 years.
The numbers x − 6, 2x and x2 are in G.P. Find nth term
If the common ratio of a G.P. is `2/3` and sum to infinity is 12. Find the first term
Find : `sum_("r" = 1)^oo (-1/3)^"r"`
Find `sum_("r" = 0)^oo (-8)(-1/2)^"r"`
If the A.M. of two numbers exceeds their G.M. by 2 and their H.M. by `18/5`, find the numbers.
Select the correct answer from the given alternative.
Which term of the geometric progression 1, 2, 4, 8, ... is 2048
Answer the following:
For a G.P. if t2 = 7, t4 = 1575 find a
Answer the following:
Find the sum of infinite terms of `1 + 4/5 + 7/25 + 10/125 + 13/6225 + ...`
At the end of each year the value of a certain machine has depreciated by 20% of its value at the beginning of that year. If its initial value was Rs 1250, find the value at the end of 5 years.
Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.
If in a geometric progression {an}, a1 = 3, an = 96 and Sn = 189, then the value of n is ______.
