In a GP of 7 terms, the last term is (64...

In a GP of `7` terms, the last term is `(64)/(81)` and the common ratio is `(2)/(3)`. Find the 3rth term.

A

4

B

9

C

8

D

12

Text Solution

Verified by Experts

The correct Answer is:

A

Let `a` be the first term and r the common ratio of the GP.
`T_y = ar^(6) = (64)/(81) rArr a =9`
Therefore the 3rd term, `T_3 = ar^(2)`
`T_3 = 9((2)/(3))^(2) =4`.

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

PROGRESSIONS
PEARSON IIT JEE FOUNDATION|Exercise LEVEL 2|17 Videos
PERMUTATIONS AND COMBINATION
PEARSON IIT JEE FOUNDATION|Exercise LEVEL 3|15 Videos
REMAINDER AND FACTOR THEOREMS
PEARSON IIT JEE FOUNDATION|Exercise Level 3|10 Videos

Similar Questions

Explore conceptually related problems

Find the 7th term of the GP whose first term is 6 and common ratio is (2)/(3) .

Find the sum of n terms of G.P where first term is a and common ratio is r.

Knowledge Check

In a GP the first term is 5 and the common ratio is 2. The eighth term is

A

640

B

1280

C

256

D

160

Find the first term of a G.P., whose 8^(th) term is 192 and common ratio is 2.

A

`3/2`

B

`2/3`

C

`3`

D

`2`

Find the number of terms in the G.P. whose first term is 3 sum is (4095)/(1024) and the common ratio is 1/4 :

A

4

B

5

C

6

D

none of these

Similar Questions

Explore conceptually related problems

In a GP, the first term is 7, the last term is 448, and the sum is 889. Find the common ratio.

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

If in a G.P.the first term is 7, the last term 448, and the sum 889, find the common ratio

The first term of an A.P. is 3, the last term is 83 and the sum of all its terms is 903. Find the number of terms and the common difference of the A.P.

Find the general term of G.P. where first term is a and common ratio is r.

PEARSON IIT JEE FOUNDATION-PROGRESSIONS-LEVEL 3

The numbers h1, h2, h3, h4,..., h10 are in harmonicprogression and a1...
04:32
|
Find the value of (1+ (1)/(2))(1+(1)/(4))(1+(1)/(16))(1+(1)/(156))…...
01:11
|
The ratio of the sum of n terms of two arithmetic progressions is give...
04:58
|
There are n arithmetic means (were n in N) between 11 and 53 such that...
03:49
|
If x= (1)/(sqrt2) + (1)/(2) + (1)/(2sqrt2) +… + oo, then find the val...
00:53
|
In a GP of 6 terms, the first and last terms are (x^(3))/(y^(2)) and ...
02:03
|
If x = 3+ (3)/(y) + (3)/(y^(2)) + (3)/(y^(3)) + … + oo, then y= .
02:16
|
Find the sum of (0.3)/(0.5) + (0.33)/(0.55) + (0.333)/(0.555) + … to ...
02:21
|
In a GP, if the fourth terms is the square of the second term, then th...
01:32
|
For which of the following values of x is (0^(@) lt x lt 90^(@)) 16^(1...
00:45
|
If t2 and t3 of a GP are p and q, respectively, then t5= .
Text Solution
|
If a, b, c, d are in GP, then (b+c)^(2)= .
03:17
|
a, b, c are in GP. If a is the first term and c is the common ratio, ...
01:03
|
In a GP of 7 terms, the last term is (64)/(81) and the common ratio is...
02:03
|
An AP starts with a positive fraction and every alternate term is an i...
03:14
|
If the sum of 16 terms of an AP is 1624 and the first term is 500 time...
02:15
|
Find the sum of the series 1+ (1+2) + (1+2+3) + (1+2 + 3 +4)+ … + (1+2...
05:00
|
Evaluate sum2^(i), where i=2, 3, 4, … , 10.
02:32
|