Study "RR RR RRR ORR objective Mathematics for B.5,8.Arch, Intranc", a flashcard deck on FORKSAI.
What defines a sequence of real numbers?
A sequence of real numbers is a function (rule) whose domain is the set of all natural numbers and whose range is a subset of R. It is essentially a function on the set of positive integers.
Explain the difference between a finite and an infinite sequence.
A sequence with a finite number of terms is called a finite sequence. If a sequence does not have a finite number of terms, it is considered an infinite sequence.
What is an arithmetic sequence (A.P.)?
An arithmetic sequence is a sequence where there is a uniform common difference between consecutive terms. This means that each term after the first is obtained by adding a constant value to the preceding term.
MCQ-STYLE: If the mth term of an A.P. is n and the nth term is m, what is the rth term?
B
What is the formula for the sum of the first n terms of an A.P. (S_n)?
The sum of the first n terms of an A.P. is given by the formula S_n = n/2 * [2a + (n-1)d], where 'a' is the first term, 'd' is the common difference, and 'n' is the number of terms.
MCQ-STYLE: If a, b, c are in A.P., then 3^a, 3^b, 3^c are in which type of sequence?
B
Define a geometric sequence (G.P.) and its nth term.
A geometric sequence is a sequence where there is a uniform common ratio between any two consecutive terms. If 'a' is the first term and 'r' is the common ratio, the nth term of the series is t_n = ar^(n-1).
What is the sum to infinity of a geometric series?
The sum to infinity of a geometric series with first term 'a' and common ratio 'r' (where |r| < 1) is given by the formula S_infinity = a / (1-r).
MCQ-STYLE: If a, b, c are three unequal numbers such that a, b, c are in A.P. and (b-a), (c-b), a are in G.P., what is the ratio a:b:c?
B
How is a Harmonic Series or Sequence defined?
A harmonic series is formed by taking the reciprocal of each term of an arithmetic series. If a_1, a_2, a_3, ... are in A.P., then 1/a_1, 1/a_2, 1/a_3, ... are in H.P.