# MCQs Sequence and Series 2

This post is about an Online Quiz of sequence and series:

A sequence is an ordered set of numbers formed according to some definite rule. Let us start with the Sequence and Series Quiz.

MCQs Mathematics covers the topic of the Number system for the preparation of Intermediate mathematics.

1. Find the number of terms in an A.P. in which $a=3, d=7$, and $a_n=59$

2. The arithmetic mean between 2+\sqrt{2}$and$2-\sqrt{2}$is 3. If all the members of a sequence are real numbers then the sequence is called 4. Which of the following cannot be the term of sequence 17, 13, 9, … 5. If 5, 8 are two A.M. between$a$and$b$then$a$and$b$are 6. The sum of the series$-3+(-1)+(1) +3+5 +\cdots+ a_{16}$is 7. If the domain of a sequence is finite then the sequence is called 8. The generl term$a_n$of an A.P. is 9. The symbol used to represent the sequence$a$is 10. A sequence in which every term after the first can be obtained by adding a fixed number in the preceding term is called 11. The$n$th A.M. between$a$and$b$is 12. If in an A.P.$a_5=13$and$a_17=49$, then$a_15=?$13. If$S_2, S_3, S_5$are the sums of$2n, 3n, 5n$terms of an A.P. then which one is true 14. If$a_{n-2}=3n-11$then$n$th term will be 15. The number of terms of the series$-7+(-5)+(-3)+\cdots$amount to 65 16. The A.M. between$1-x+x^2$and$1+x-x^2$is 17. If$\frac{1}{a}, \frac{1}{b}$and D\frac{1}{c}$ are in A.P. then which one is true:

18. The sequence $1, \frac{3}{2}, \frac{5}{4}, \frac{7}{8}, \cdots$, then $a_7=?$

19. Sequence is also called

20. A sequence is a function whose domain is

A sequence can be defined as a function whose domain is a subset of natural numbers. Mathematically, the sequence is denoted by $\{a_n\}$ where $n\in N$.

Some examples of sequence are:

• $1,2,3,\cdots$
• $2, 4, 6, 8, \cdots$
• $\frac{1}{3}, \frac{1}{5}, \frac{1}{7}, \cdots$

The term $a_n$ is called the general term or $n$th term of a sequence. If all numbers of a sequence are real numbers then it is called a real sequence. If the domain of a sequence is a finite set, then the sequence is finite otherwise the sequence is infinite. An infinite sequence has no last term.

If the terms of a sequence follow a certain pattern, then it is called a progression:

• Arithmetic Progression (AP)
A sequence $\{a_n\}$ is an Arithmetic Sequence or Arithmetic Progression if the difference $a_n – a_{n-1}$ is the same for all $n \in N$ and $n>1$.
• Geometric Progression (GP)
A sequence $\{a_n\}$ in which $\frac{a_n}{a_{n-1}}$ is same non-zero number for al l$n\in N$ and $n>1$ is called Geometric Sequence or Geometric Progression.
• Harmonic Progression (HP)
A Harmonic Progression is a sequence of numbers whose reciprocals form an Arithmetic Progression. A general form of Harmonic Progression is $\frac{1}{a_1}, \frac{1}{a_1+d}, \frac{1}{a_1+2d}, \cdots$, where $a_n=\frac{1}{a_1+(n-1)d}$

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