Which term of the following sequences:
(a) The given sequence is
Here, a = 2 and r =
Let the nth term of the given sequence be 128.
Thus, the 13th term of the given sequence is 128.
(b) The given sequence is
Here, a=
Let the nth term of the given sequence be 729.
Thus, the 12th term of the given sequence is 729.
(c) The given sequence is
Here,
a=
Let the nth term of the given sequence be .
Thus, the 9th term of the given sequence is .
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.
The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
For what values of x, the numbers are in G.P?
An experiment consists of recording boy-girl composition of families with 2 children.
(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
(ii) What is the sample space if we are interested in the number of girls in the family?
Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.
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.
Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.
Find the sum to n terms of the series whose nth terms is given by n2 + 2n