English

The numbers x − 6, 2x and x2 are in G.P. Find 1st term - Mathematics and Statistics

Advertisements
Advertisements

Question

The numbers x − 6, 2x and x2 are in G.P. Find 1st term

Sum
Advertisements

Solution

t1 = x – 6

= 10 – 6

= 4

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Sequences and Series - Exercise 2.1 [Page 28]

APPEARS IN

RELATED QUESTIONS

Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.


Which term of the following sequence: 

`2, 2sqrt2, 4,.... is 128`


Which term of the following sequence:

`1/3, 1/9, 1/27`, ...., is `1/19683`?


Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).


Insert two numbers between 3 and 81 so that the resulting sequence is G.P.


Find:

the 10th term of the G.P.

\[- \frac{3}{4}, \frac{1}{2}, - \frac{1}{3}, \frac{2}{9}, . . .\]

 


The fourth term of a G.P. is 27 and the 7th term is 729, find the G.P.


In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.


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:

\[\frac{2}{9} - \frac{1}{3} + \frac{1}{2} - \frac{3}{4} + . . . \text { to 5 terms };\]


Evaluate the following:

\[\sum^{10}_{n = 2} 4^n\]


The 4th and 7th terms of a G.P. are \[\frac{1}{27} \text { and } \frac{1}{729}\] respectively. Find the sum of n terms of the G.P.


Find the sum :

\[\sum^{10}_{n = 1} \left[ \left( \frac{1}{2} \right)^{n - 1} + \left( \frac{1}{5} \right)^{n + 1} \right] .\]


Let an be the nth term of the G.P. of positive numbers.

Let \[\sum^{100}_{n = 1} a_{2n} = \alpha \text { and } \sum^{100}_{n = 1} a_{2n - 1} = \beta,\] such that α ≠ β. Prove that the common ratio of the G.P. is α/β.


Express the recurring decimal 0.125125125 ... as a rational number.


Find the rational number whose decimal expansion is `0.4bar23`.


Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.


Find k such that k + 9, k − 6 and 4 form three consecutive terms of a G.P.


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 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.


Write the product of n geometric means between two numbers a and b

 


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 pq be two A.M.'s and G be one G.M. between two numbers, then G2


The product (32), (32)1/6 (32)1/36 ... to ∞ is equal to 


Check whether the following sequence is G.P. If so, write tn.

7, 14, 21, 28, …


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 n years.


For a G.P. if a = 2, r = 3, Sn = 242 find n


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 G.P. If t4 = 16, t9 = 512, find S10


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 common ratio of the G.P is 5, 5th term is 1875, the first term is -


The sum of 3 terms of a G.P. is `21/4` and their product is 1 then the common ratio is ______.


Answer the following:

Find the sum of the first 5 terms of the G.P. whose first term is 1 and common ratio is `2/3`


Answer the following:

Find five numbers in G.P. such that their product is 243 and sum of second and fourth number is 10.


Answer the following:

Find k so that k – 1, k, k + 2 are consecutive terms of a G.P.


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.


Let `{a_n}_(n = 0)^∞` be a sequence such that a0 = a1 = 0 and an+2 = 2an+1 – an + 1 for all n ≥ 0. Then, `sum_(n = 2)^∞ a^n/7^n` is equal to ______.


The sum of the infinite series `1 + 5/6 + 12/6^2 + 22/6^3 + 35/6^4 + 51/6^5 + 70/6^6 + ....` is equal to ______.


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 ______. 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×