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## Progressions

Question 6 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

Find the 15th term of the sequence 20, 15, 10....

-55 | |

-50 | |

-45 | |

0 |

Question 6 Explanation:

15

^{th}term = a+14d = 20+14*(-5) = 20-70 = -50.Question 7 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

7 | |

6 | |

4 | |

5 |

Question 7 Explanation:

1

^{st}Method:8th term = a+7d = 39 ..... (i)

12th term = a+11d = 59 ..... (ii)

(i)-(ii);

Or, a+7d-a-11d = 39-59; Or, 4d = 20;

Or, d = 5;

Hence, a+7*5 = 39;

Thus, a = 39-35 = 4.

2nd Method (Thought Process):

8th term = 39;

And, 12th term = 59;

Here, we see that 20 is added to 8th term 39 to get 12th term 59 i.e. 4 times the common difference is added to 39.

So, CD = 20/4 = 5.

Hence, 7 times CD is added to 1st term to get 39. That means 4 is the 1st term of the AP.

Question 8 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

A square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely. If a side of the first square is 4 cm, determine the sum of the areas all the square.

32 Cm ^{2} | |

16 Cm ^{2} | |

64 Cm ^{2} | |

20 Cm ^{2} |

Question 8 Explanation:

\begin{align} & {\text{Side of the first square is }}4{\text{ }}cm. \cr & {\text{side of second square}} \cr & = 2\sqrt 2 \, cm \cr & {\text{Side}}\, {\text{of}}\, {\text{third}}\, {\text{square}} \cr & = 2\, cm \cr & {\text{and}}\, {\text{so}}\, {\text{on}}{\text{.}}\, i.e. \cr & 4, \, 2, \, \sqrt 2, \, \sqrt 2, \, 1\, ..... \cr & {\text{Thus, area of these square will be}}, \cr & = 16, \, 8, \, 4, \, 2, \, 1, \, \frac{1}{2}..... \cr & {\text{Hence, Sum of the area of first, second, third square}}.... \cr & = 16 + 8 + 4 + 2 + 1 + \, ..... \cr & = \left[ {\frac{{16}}{{\left\{ {1 - \left( {\frac{1}{2}} \right)} \right\}}}} \right] \cr & = 32\, c{m^2} \cr\end{align}

Question 9 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. initially there is one newly born bacteria at time

**t = 0**, the find the total number of live bacteria just after 10 seconds :3 ^{10} /2 | |

243 *(3 ^{5} -1) | |

3 ^{10} - 2^{10} | |

3 ^{10} -2^{5} |

Question 9 Explanation:

Total number of bacteria after 10 seconds,

= 3^{10} - 3^{5}

= 3^{5} *(3^{5} -1)

= 243 *(3^{5} -1)

Since, just after 10 seconds all the bacterias (i.e. 3^{5} ) are dead after living 5 seconds each.

Question 10 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

640 | |

690 | |

680 | |

765 |

Question 10 Explanation:

\begin{align} & {1^{st}}\, {\text{Method}}: \cr & {1^{st}}\, {\text{term}} = 5; \cr & {3^{rd}}\, {\text{term}} = 15; \cr & {\text{Then}}, \, d = 5; \cr & {16^{th}}\, {\text{term}} = a + 15d \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 5 + 15 \times 5 \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 80 \cr & {\text{Sum}} = \left\{ {n \times \frac{{\left( {a + l} \right)}}{2}} \right\} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \left\{ {{\text{no}}{\text{.}}\, {\text{of}}\, {\text{terms}} \times \frac{{\left( {{\text{first}}\, {\text{term + last}}\, {\text{term}}} \right)}}{2}} \right\} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, = \left\{ {16 \times \frac{{\left( {5 + 80} \right)}}{2}} \right\} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, \, = 680 \cr & \cr & {2^{nd}}\, {\text{Method}}\, ({\text{Thought}}\, {\text{Process}}): \cr & {\text{Sum}} = {\text{number}}\, {\text{of}}\, {\text{terms}} \times {\text{average}}\, {\text{of}}\, {\text{that}}\, {\text{AP}} \cr & {\text{Sum}} = 16 \times \left\{ {\frac{{\left( {5 + 80} \right)}}{2}} \right\} \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, = 16 \times 45 \cr & \, \, \, \, \, \, \, \, \, \, \, \, \, = 680 \cr\end{align}

There are 10 questions to complete.