Series - 01

1.    114        115         107         134        70        ?     [Ans:-(3)]

(1) 140   (2)35         (3)195       (4)150        (5) None of these      

                                                                                                                  

2.    2         6        33         49         174         210        ?     [Ans:-(1)]

(1) 553      (2) 259       (3) 426    (4) 274      (5) None of these    

                                                                                          

3.    64       128      92        220        148        404       ?     [Ans:-(4)]                      

(1) 332      (2) 296      (3) 276        (4) 260     (5) None of these          

4.     2          21          138           705          ?       [Ans:-(5)]            

(1) 2386    (2) 3540    (3) 2820       (4) 3236   (5) None of these                                                                                                          

5.     9        ?       20        31        51       82       133    [Ans:-(5)]            

(1) 13     (2) 18      (3) 12     (4) 15      (5) None of thee 

Solution:

              +1³        -2³           +3³          -4³       +5³                                      

1)    114         115         107         134         70        ?     [? = 195 Ans.]

         +2²      +3³       +4²        +5³         +6²          +7³                                      

2)    2         6         33          49         174         210        ?     [? = 553 Ans.]

           +64         -36        +128       -72         +256      -144                                        

3)    64         128          92          220        148        404       ?     [? = 260 Ans.]

          ×7 + 7×1      ×6 + 6×2        ×5 + 5×3        ×4 + 4×4                                                      

4)     2                 21                 138                 705                ?       [? = 2836 Ans.]  

                         (9+?=20)     (?+20=31)     (20+31=51)  (31+51=81)     (51+82=133)       

5)     9               ?                 20                  31                  51                   82                   133    

[? = 11 Ans.]   

Detailed Explanation:

1) This is an ups and downs series. Changes are respectively +1, -8, +27, -+64, -125, and so on. That is, + 1³, - 2³, +3³, -4³, +5³ and so on. So, no. at the question mark will be 70 + 125 = 195 Ans.

2) The changes are respectively +4, +27, +16, +125, +36, +343 and so on. That is, +2², +3³, +4², +5³, +6², +7³ and so on. So, no. at the question mark will be 210 + 343 = 553 Ans.  

3) Here, the changes are respectively +64, -36, +128, -72, +256, -144 and so on. Relation exist between the changes at the odd places as +64, +128, +256,….. and at the even places as -36, -72, -144,…… So, no. at the question mark will be 404 - 144 = 260 Ans.  

4) In this series, the slop is as ×7, ×6, ×5, ×4, ×3, ×2, ×1. Also, 7, 12, 15, 16,….. are added that can be written as 7×1, 6×2, 5×3, 4×4, 3×5, 2×6, 1×7. Here, the numbers of the products are complimentary with respect to 8, that means, the sum is 8.

7+1=8, 6+2=8, 5+3=8, 4+4=8, 3+5=8, 2+6=8, 1+7=8. So, no. at the question mark will be 705 ×4 + 4 ×4 = 2836 Ans.

5) In this series, any number in the series is just the sum of its previous two numbers. As for example, (9+?=20), (?+20=31), (20+31=51), (31+51=81), (51+82=133). So, no. at the question mark 11 Ans.