Practice AP Inter 1st Year Maths Study Material Chapter 8 Sequences and Series MCQ to identify your strengths and weak areas.
AP Inter 1st Year Maths Sequences and Series MCQ
Question 1.
Which of the following is finite sequence ?
1) 48, 24, 12, ………..
2) 1, 2, 3, …….
3) 2, 4, 6, 8, 10 ………..
4) 2, 3, 5, 7, 11, 13, …….
Answer:
3) 2, 4, 6, 8, 10 ………..
Explanation:
2, 4, 6, 8, 10 is a finite sequence.
Question 2.
Which of the following relation gives Fibonacci sequence ?
1) an = an-1 + an-2, n > 2
2) an-1 = an + an-2, n > 2
3) an-2 = an + an-1, n> 2
4) an = an+1 + an-2, n > 2
Answer:
1) an = an-1 + an-2, n > 2
Explanation:
Relation of fibonacci sequence is an = an-1 + an-2, n > 2
Question 3.
The first term of Fibonacci sequence is
1) 0
2) 1
3) 2
4) 3
Answer:
2) 1
Explanation:
The first term of fibonacci sequence is “1”.
Question 4.
If an = 4n + 6, then 15th term of the sequence is
1) 6
2) 10
3) 60
4) 66
Answer:
4) 66
Explanation:
an = 4n + 6
a15 = 4(15) + 6
= 60 + 6 = 66
Question 5.
A series can also be denoted by the symbol …………
1) πan
2) Σan
3) Φan
4) θan
Answer:
2) Σan
Explanation:
Series denoted by Σan
Question 6.
The sum of first five terms of series 2 + 4 + 6 + ….. is
1) 14
2) 16
3) 20
4) 30
Answer:
4) 30
Explanation:
Given series 2 + + 6 + ………..
Sum of even number Sn = n(n + 1)
S5 = 5(5 + 1) = 5.(6) = 30
Question 7.
\(\sum_{n=1}^4\) 2n + 3 = ……….
1) 5
2) 12
3) 21
4) 32
Answer:
4) 32
Explanation:
\(\sum_{n=1}^4\) 2n + 3, If n = 1, 2, 3, 4; Series is 5, 7, 9, 11 …… ; S4 = 5 + 7 + 9 + 11 = 32
Question 8.
If an+1 = an. r then the sequence is called
1) Arithmetic progression
2) Geometric progression
3) Harmonic progression
4) Special progression
Answer:
2) Geometric progression
Explanation:
an+1 = an. r is G.P.
Question 9.
The nth term of G.P. is ( 3 )
1) an = a + (n – 1) d
2) an = a + nd
3) an = a . rn-1
4) an = arn
Answer:
3) an = a . rn-1
Explanation:
nth term of G.P. is an = a . rn-1
Question 10.
If r = 1 in G.P. then the sum of first n terms is
1) na
2) a/n
3) (n – 1) a
4) (n + 1) a
Answer:
1) na
Explanation:
If r = 1, the sum of first n terms = na
Question 11.
If 4, 8, 16, 32 are in G.P. then the sum upto 5th term is
1) 16
2) 64
3) 128
4) 124
Answer:
4) 124
Explanation:
4, 8, 16, 32, are in G.P; a = 4, r = 2
S5 = \(\frac{4\left(2^5-1\right)}{2-1}=\frac{4(32-1)}{1}\) = 4(31) = 124
Question 12.
The Sum of series 1 + \(\frac{1}{2}+\frac{1}{4}\) + …….. upto 6 terms is
1) \(\frac{63}{32}\)
2) \(\frac{32}{63}\)
3) \(\frac{26}{53}\)
4) \(\frac{53}{26}\)
Answer:
1) \(\frac{63}{32}\)
Explanation:
Series 1 + \(\frac{1}{2}+\frac{1}{4}\) + …….. upto 6 terms
Sum of 6 terms = \(\frac{\left(1-\left(\frac{1}{2}\right)^6\right)}{1-\frac{1}{2}}\)
= 2(1 – \(\frac{1}{64}\))
= 2 – \(\frac{1}{32}=\frac{64-1}{32}=\frac{63}{32}\)
Question 13.
The geometric mean of 3 and 12 is ………….
1) 4
2) 6
3) 9
4) 12
Answer:
2) 6
Explanation:
Geometric mean of 3 and 12 = \(\sqrt{3 \times 12}=\sqrt{36}\)
= 6
Question 14.
If A.M of two numbers is \(\frac{15}{2}\) and their G.M is 6 then the two numbers are
1) 6 and 8
2) 12 and 3
3) 24 and 6
4) 27 and 3
Answer:
2) 12 and 3
Explanation:
Let the two numbers be and b
A.M = \(\frac{15}{2} \Rightarrow \frac{a+b}{2}=\frac{15}{2}\)
⇒ a + b = 15 ……….(1)
G. M = 6 ⇒ \(\sqrt{\mathrm{ab}}\)
⇒ ab = 36
a – b = \(\sqrt{(a+b)^2-4 a b}=\sqrt{225-144}=\sqrt{81}\)
a – b = 9 …(2)
(1) + (2) ⇒ a = 12, b = 3
Question 15.
If A means arithmetic mean and G means geometric mean then which of the following is true ?
1) A > G
2) A ≥ G
3) G > A
4) G ≥ A
Answer:
2) A ≥ G
Explanation:
A ≥ G
Question 16.
The ratio of A.M. and G.M of two positive numbers a and b is 5 : 3. Then the ratio of a to b is ( 1 )
1) 9 : 1
2) 3 : 5
3) 1 : 9
4) 3 : 1
Answer:
\(\frac{A \cdot M}{G \cdot M}=\frac{5}{3} \Rightarrow \frac{a+b}{2 \sqrt{a b}}=\frac{5}{3}\)
⇒ 9(a + b)2 = 25 (4ab)
⇒ 9a2 + 18ab + 9b2 = 100 ab
⇒ 9a2 – 82ab + 9b2 = 0
⇒ (9a – b) (a – 9b) = 0
9a-b = 0
9a = b
\(\frac{a}{b}=\frac{1}{9}\)
a – 9b = 0
a = 9b
\(\frac{a}{b}=\frac{9}{1}\)
∴ a : b = 9 : 1 (∵ a > b)