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## Progressions

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Question 1 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] |

**The 7**

^{th}and 21^{st}terms of an AP are 6 and -22 respectively. Find the 26^{th}term.-32 | |

-34 | |

-10 | |

-16 |

Question 1 Explanation:

7

^{th}term = 6; 21^{st} term = -22;

That means, 14 times common difference or -28 is added to 6 to get -22;

Thus, d = -2;

7^{st} term = 6 = a+6d;

Or, a+(6*-2) = 6;

Or, a = 18;

26^{st} term = a+25d = 18-25*2 = -32.

Question 2 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] |

**Find the n**

^{th}term of the following sequence :** 5 + 55 +555 + . . . . T _{n} **

(5/9)*(10^{n} - 1) | |

5^{n}(10^{n} - 1) | |

(5/9)^{n} *10^{n} - 1) | |

5(10^{n} - 1) |

Question 2 Explanation:

\begin{align} & {\text{We will it through option checking method}}: \cr & \left( {\frac{5}{9}} \right) \times \left( {{{10}^n} - 1} \right) \cr & {\text{We}}\, {\text{put}}\, n = 1, \cr & \left( {\frac{5}{9}} \right) \times \left( {{{10}^1} - 1} \right) = 5 \cr & n = 2\left( {\frac{5}{9}} \right) \times \left( {{{10}^2} - 1} \right) = 55 \cr & n = 3\left( {\frac{5}{9}} \right) \times \left( {{{10}^3} - 1} \right) = 555 \cr & {\text{It means Option C is satisfying the sequence so the}} \cr & {n^{th}}\, {\text{term}}\, {\text{would}}\, {\text{be}}\, \left( {\frac{5}{9}} \right) \times \left( {{{10}^n} - 1} \right) \cr\end{align}

Question 3 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] |

**How many terms are there in 20, 25, 30..... 140**

23 | |

25 | |

22 | |

24 |

Question 3 Explanation:

\begin{align} & {\text{Number}}\, {\text{of}}\, {\text{terms}}, \cr & = \left\{ {\frac{{\left( {{1^{st}}\, t{\text{erm - last}}\, {\text{term}}} \right)}}{{{\text{common}}\, {\text{difference}}}}} \right\} + 1 \cr & = \left( {140 - \frac{{20}}{5}} \right) + 1 \cr & = \left( {\frac{{120}}{5}} \right) + 1 \cr & = 24 + 1 \cr & = 25 \cr\end{align}

Question 4 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] |

**The first term of an Arithmetic Progression is 22 and the last term is -11. If the sum is 66, the number of terms in the sequence are:**

8 | |

9 | |

12 | |

10 |

Question 4 Explanation:

\begin{align} & {\text{Number}}\, {\text{of}}\, {\text{terms}} = n\, \left( {let} \right) \cr & {\text{First}}\, {\text{term}}\, \left( a \right) = 22 \cr & {\text{Last}}\, {\text{term}}\left( l \right) = - 11 \cr & {\text{Sum}} = 66 \cr & {\text{Sum}}\, {\text{of}}\, {\text{an}}\, {\text{AP}}\, {\text{is}}\, {\text{given}}\, {\text{by}}: \cr & = {\text{Number}}\, {\text{of}}\, {\text{terms}} \times \left\{ {\frac{{\left( {{\text{First}}\, {\text{term}} + {\text{Last}}\, {\text{term}}} \right)}}{2}} \right\} \cr & 66 = n \times \left\{ {\frac{{\left( {a + l} \right)}}{2}} \right\} \cr & 66 = n \times \frac{{\left( {22 - 11} \right)}}{2} \cr & 66 = n \times \left( {\frac{{11}}{2}} \right) \cr & n = \frac{{\left( {66 \times 2} \right)}}{{11}} \cr & n = 12 \cr & {\text{No}}{\text{.}}\, {\text{of}}\, {\text{terms}} = 12 \cr\end{align}

Question 5 [CLICK ON ANY CHOICE TO KNOW MCQ multiple objective type questions RIGHT ANSWER] |

**If the fifth term of a GP is 81 and first term is 16, what will be the 4**

^{th}term of the GP?24 | |

18 | |

27 | |

54 |

Question 5 Explanation:

\begin{align} & {5^{th}}\, {\text{term}}\, {\text{of}}\, {\text{GP}} \cr & = a{r^{5 - 1}} \cr & = 16 \times {r^4} \cr & = 81 \cr & {\text{Or}}, \, r = {\left( {\frac{{81}}{{16}}} \right)^{\frac{1}{4}}} = \frac{3}{2} \cr & {4^{th}}\, {\text{term}}\, {\text{of}}\, {\text{GP}} \cr & = a{r^{4 - 1}} \cr & = 16 \times {\left( {\frac{3}{2}} \right)^3} \cr & = 54 \cr\end{align}

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