If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.
The first term of the G.P is a and the last term is b.
Therefore, the G.P. is a, ar, ar2, ar3, … arn–1, where r is the common ratio.
b = arn–1 … (1)
P = Product of n terms
= (a) (ar) (ar2) … (arn–1)
= (a × a ×…a) (r × r2 × …rn–1)
= an r 1 + 2 +…(n–1) … (2)
Here, 1, 2, …(n – 1) is an A.P.
∴1 + 2 + ……….+ (n – 1)
Thus, the given result is proved.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
A die is thrown. Describe the following events:
(i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3
(iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not less than 3
Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F’, F’
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
For what values of x, the numbers are in G.P?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.
Find a point on the x-axis, which is equidistant from the points (7, 6) and (3, 4).
2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
Thank you
Very good.. thanks for the easiest way.
Very good
Please change the colour of this page And nice explanation
Why n-1/2 is taken instead of n/2
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