The sum of first three terms of a G.P. is and their product is 1. Find the common ratio and the terms.
Let be the first three terms of the G.P.
From (2), we obtain
a3 = 1
⇒ a = 1 (Considering real roots only)
Substituting a = 1 in equation (1), we obtain
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.
A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
Find the sum to n terms in the geometric progression x3, x5, x7 ... (if x ≠ ±1)
A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.
If a, b, c and d are in G.P. show that
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
Which of the following sentences are statements? Give reasons for your answer.
(i) There are 35 days in a month.
(ii) Mathematics is difficult.
(iii) The sum of 5 and 7 is greater than 10.
(iv) The square of a number is an even number.
(v) The sides of a quadrilateral have equal length.
(vi) Answer this question.
(vii) The product of (–1) and 8 is 8.
(viii) The sum of all interior angles of a triangle is 180°.
(ix) Today is a windy day.
(x) All real numbers are complex numbers.