Let be the nth term of a G.P. of positive terms. If is equal to :
Option: 1
Option: 2
Option: 3
Option: 4
150
View Full Answer(5)The sum is
Option: 1 1540
Option: 2 1680
Option: 3 1260
Option: 4 1450
Sum of Common Series
Sum of the square of first n-natural numbers
Now,
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Let be such that for all and are in A.P., then the minimum value of is :
Option: 1
Option: 2
Option: 3
Option: 4
Important Properties of an AP
If a, b, c are in AP, then 2b = a + c
and
AM ≥ GM
Applying this to given question,
Correct Option (3)
View Full Answer(1)Five numbers are in A.P., whose sum is 25 and product is 2520. If one of these five numbers is , then the greatest number amongst them is :
Option: 1
Option: 2
Option: 3
Option: 4
Five terms are in AP
Let terms are a-2d, a-d, a, a+d, a+2d
Sum of the terms = 5a = 25
So, a=5
Product of the terms
(a-2d) (a-d) (a+d) (a+2d) a = 2520
Putting a = 5
(25 - 4d2) (25 - d2) = 504
Putting d2 = t
(25 - t) (25 - 4t) = 504
4t2 - 125t + 121 = 0
t = 1 or t = 121/4
d = 1 or d = -1 or d= 11/2 or d = -11/2
But -1/2 can be a term of AP only for d= 11/2 or d = -11/2
Using d = 11/2
Greatest term = a+ 2d = 16
Correct Option (1)
View Full Answer(1)The greatest positive integer k, for which is a factor of the sum is :
Option: 1
Option: 2
Option: 3
Option: 4
Sum of n-term of a GP
Let Sn be the sum of n terms of the G.P. with the first term ‘a’ and common ratio ‘r’. Then
The above formula does not hold for r = 1, For r = 1 the sum of n terms of the G.P. is .
Now,
As xn - yn is always divisible by (x - y), so is an integrer
Hence, K=63
Correct Option (4)
View Full Answer(1)The sum, is equal to _______.
Option: 1
Option: 3
Option: 5
Option: 7
Sum of Common Series
Sum of the square of first n-natural numbers
Sum of the cube of first n-natural numbers
-
Now,
Correct Option (3)
View Full Answer(1)If the 10th term of an A.P. is and its 20th term is , then the sum of its first 200 term is :
Option: 1
Option: 3
Option: 5
Option: 7
General Term of an AP
nth term (general term) of the A.P. is .
Sum of n terms of an AP
The sum, Sn of n terms of an AP with the first term ‘a’ and common difference ‘d’ is given by
Now,
Correct Option (4)
View Full Answer(1)Let be a G.P. such that and If then is equal to :
Option: 1
Option: 2
Option: 3
Option: 4
Given,
a1 + a2 = 4 ………(i)
a3 + a4 = 16 …….(ii)
On dividing these
Correct Option (3)
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