Question

choose the correct choice in the following and justify

Answer 1

(1) Given 30th term of the AP:10,7,4 is.

Answer: Option (C) : - 77

Explanation : 

Given first term a = 10,

          Last term n = 30.

          common difference d = 7 - 10 = -3.

We know that sum of n terms an = a + (n - 1) * d

                                                  a30 = 10 + (30 - 1) * (-3)

                                                          = 10 + 29 * (-3)

                                                          = 10 + (-87)

                                                         = -77.

Therefore the 30th term of the AP is  -77.



(2) Given 11th term of the AP is -3,-1/2,2.... is.

Answer : Option (B) :- 22

Explanation : 

Given first term a = -3.
 
          Last term n = 11.

         common difference d = -1/2 + 3

                                              = 6 - 1/2

                                              = 5/2.


We know that nth term of an AP an = a + (n - 1) * d

                                                       a11 = -3 + (11 - 1) * 5/2

                                                             = - 3 + 10 * 5/2

                                                             = - 3 + 25

                                                             = 22.


Therefore the 11th term of the AP is 22.


Hope this helps!                            

Answer 2

according to me, 2. i) (A)
ii) (A)