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Algebra: Sequence and Series Test-2

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Question 1

The sum (5^{3} + 6^{3} + ……10^{3}) is equal to

A

2295

B

2425

C

2495

D

2925

Question 1 Explanation:

Let p = Sum of cubes of all natural numbers till 10 and q = sum of cubes of all natural numbers till 4
The given expression=p-q $ \begin{array}{l}{{\left( \frac{10(10+1)}{2} \right)}^{2}}-{{\left( \frac{4(4+1)}{2} \right)}^{2}}\\={{55}^{2}}-{{10}^{2}}\\=65X45\\=2925\end{array}$

Question 2

The next term of the sequence 1, 2, 5, 26……. is:

A

677

B

47

C

50

D

152

Question 2 Explanation:

The general term is square of previous term +1. Thus the next term is 26^{2}+1= 677.

Question 3

The missing term in the sequence 0, 3, 8, 15, 24, …… 48 is

A

35

B

30

C

36

D

39

Question 3 Explanation:

The n^{th} term is n^{2}-1. Thus the 6^{th} term is 6^{2}-1=35.

Question 4

If 1^{3} + 2^{3} + 3^{3} + ……..+ 10^{3} = 3025, then find the value of 2^{3} + 4^{3} + 6^{3} + …..+ 20^{3}