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Algebra: Sequence and Series Test-1

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Question 1

The next number of the sequence 3, 5, 9, 17, 33 ……..is:

A

65

B

60

C

50

D

49

Question 1 Explanation:

The sequence is 2^{n}+1
Thus the next term is 6^{th} term.
2^{n}+1 = 2^{6}+1 = 64+1=65.
The correct option is (a)

Question 2

The next term of the sequence$ \displaystyle \frac{1}{2},\,\,3\frac{1}{4},\,\,6,\,\,8\frac{3}{4}........is:$

A

$ \displaystyle 10\frac{1}{4}$

B

$ \displaystyle 10\frac{3}{4}$

C

$ \displaystyle 11\frac{1}{4}$

D

$ \displaystyle 11\frac{1}{2}$

Question 2 Explanation:

The general term is $ \frac{2+11(n-1)}{4}$ The 5^{th} term will be $latex \frac{46}{4}=\frac{23}{2}=11\frac{1}{2}$

Question 3

Find the missing number of the sequence: “3, 14, 25, 36, 47, ? ”

A

1114

B

1111

C

1113

D

None of these

Question 3 Explanation:

The general term is 3+11(n-1). The 6^{th} term is 58.

Question 4

The sum (101+ 102 + 103 + ….. + 200) is equal to:

A

15000

B

15025

C

15050

D

25000

Question 4 Explanation:

The given expression = total of all natural numbers till
200- total of all natural numbers till 100. $ \begin{array}{l}=\frac{200(200+1)}{2}-\frac{100(100+1)}{2}\\=20100-5050\\=15050\end{array}$

Question 5

Which term of the series 72, 63, 54………..is zero?

A

11^{th}

B

10^{th}

C

9^{th}

D

8^{th}

Question 5 Explanation:

The general term is 72-9(n-1). Thus,$ \displaystyle \begin{array}{l}72-9\left( n-1 \right)=0\\=>72=9(n-1)\\=>n-1=8\\=>n=9\end{array}$.

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