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## Algebra: Sequence and Series Test-2

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Question 1 |

The sum (5

^{3}+ 6^{3}+ â€¦â€¦10^{3}) is equal to2295 | |

2425 | |

2495 | |

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}$

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, 26â€¦â€¦. is:

1, 2, 5, 26â€¦â€¦. is:

677 | |

47 | |

50 | |

152 |

Question 2 Explanation:

The general term is square of previous term +1.

Thus the next term is 26

Thus the next term is 26

^{2}+1= 677.Question 3 |

The missing term in the sequence

0, 3, 8, 15, 24, â€¦â€¦ 48 is

0, 3, 8, 15, 24, â€¦â€¦ 48 is

35 | |

30 | |

36 | |

39 |

Question 3 Explanation:

The n

Thus the 6

^{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}+ â€¦â€¦..+ 10^{3}= 3025, then find the value of 2^{3}+ 4^{3}+ 6^{3}+ â€¦..+ 20^{3}6050 | |

9075 | |

12100 | |

24200 |

Question 4 Explanation:

$ \displaystyle \begin{array}{l}{{2}^{3}}+{{4}^{3}}+{{6}^{3}}+.......+{{20}^{3}}\\={{\left( 2\times 1 \right)}^{3}}+{{\left( 2\times 2 \right)}^{3}}+{{\left( 2\times 3 \right)}^{3}}+.......+{{\left( 2\times 10 \right)}^{3}}\\=8\times {{1}^{3}}+8\times {{2}^{3}}+8\times {{3}^{3}}.......+8\times {{10}^{3}}\\=8\times \left[ {{1}^{3}}+{{2}^{3}}+{{3}^{3}}+{{4}^{3}}+........+{{10}^{3}} \right]\\=8\times 3025=24200\\\left[ \because \,\,\,{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+.........+{{10}^{3}}=3025\,\,\left( given \right) \right]\end{array}$

Question 5 |

What is the 507

1, â€“1, 2, â€“2, 1, â€“1, 2, â€“2, 1â€¦..?

^{th}term of the sequence1, â€“1, 2, â€“2, 1, â€“1, 2, â€“2, 1â€¦..?

â€“1 | |

1 | |

â€“2 | |

2 |

Question 5 Explanation:

The sequence 1,-1, 2,-2 repeats.

Thus we just need to find the (507 mod 4) = 3

Thus the 507

Thus we just need to find the (507 mod 4) = 3

^{rd}term of the sequence.Thus the 507

^{th}term will be 2.
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