हिंदी

Find : the 8th Term of the G.P. 0.3, 0.06, 0.012, ... - Mathematics

Advertisements
Advertisements

प्रश्न

Find :

the 8th term of the G.P. 0.3, 0.06, 0.012, ...

Advertisements

उत्तर

Here,

\[\text { First term }, a = 0 . 3\]

\[\text { Common ratio }, r = \frac{a_2}{a_1} = \frac{0 . 06}{0 . 3} = 0 . 2\]

\[ \therefore 8th\text { term } = a_8 = a r^{(8 - 1)} = 0 . 3(0 . 2 )^7 \]

\[\text { Thus, the 8th term of the given GP is } 0 . 3(0 . 2 )^7 .\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 20: Geometric Progression - Exercise 20.1 [पृष्ठ १०]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 20 Geometric Progression
Exercise 20.1 | Q 3.3 | पृष्ठ १०

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Which term of the following sequence: 

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


Find the sum to indicated number of terms of the geometric progressions `sqrt7, sqrt21,3sqrt7`...n terms.


Find the sum of the products of the corresponding terms of the sequences `2, 4, 8, 16, 32 and 128, 32, 8, 2, 1/2`


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.

 

Show that the sequence <an>, defined by an = \[\frac{2}{3^n}\], n ϵ N is a G.P.


Which term of the progression 0.004, 0.02, 0.1, ... is 12.5?


Find three numbers in G.P. whose sum is 65 and whose product is 3375.


Find the sum of the following series:

7 + 77 + 777 + ... to n terms;


The ratio of the sum of first three terms is to that of first 6 terms of a G.P. is 125 : 152. Find the common ratio.


Find the sum of 2n terms of the series whose every even term is 'a' times the term before it and every odd term is 'c' times the term before it, the first term being unity.


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


If a, b, c are in G.P., prove that \[\frac{1}{\log_a m}, \frac{1}{\log_b m}, \frac{1}{\log_c m}\] are in A.P.


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:

a (b2 + c2) = c (a2 + b2)


If a, b, c are in G.P., prove that the following is also in G.P.:

a2, b2, c2


If the 4th, 10th and 16th terms of a G.P. are x, y and z respectively. Prove that x, y, z are in 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 pth, qth and rth terms of an A.P. are in G.P., then the common ratio of this G.P. is


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 a = `2/3`, t6 = 162, find r.


Find four numbers in G.P. such that sum of the middle two numbers is `10/3` and their product is 1


If p, q, r, s are in G.P. show that p + q, q + r, r + s are also in G.P.


The number of bacteria in a culture doubles every hour. If there were 50 bacteria originally in the culture, how many bacteria will be there at the end of 5th hour?


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


For a G.P. if S5 = 1023 , r = 4, Find a


If Sn, S2n, S3n are the sum of n, 2n, 3n terms of a G.P. respectively, then verify that Sn (S3n – S2n) = (S2n – Sn)2.


Express the following recurring decimal as a rational number:

`2.3bar(5)`


Find : `sum_("n" = 1)^oo 0.4^"n"`


Select the correct answer from the given alternative.

Which term of the geometric progression 1, 2, 4, 8, ... is 2048


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


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 ______.


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))`


If `e^((cos^2x + cos^4x + cos^6x + ...∞)log_e2` satisfies the equation t2 – 9t + 8 = 0, then the value of `(2sinx)/(sinx + sqrt(3)cosx)(0 < x ,< π/2)` is ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×