AIEEE Questions

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2.5 × 1 + 1 = 3.5

3.5 × 2 + 2 = 9

9 × 4 + 4 = 40

40 × 8 + 8 = 328

Dr. G. D. Bist, Guinness Record Holder, the first-ever Ph.D. in Stenography in the world.

He had achieved a highest speed of 250 w.p.m. in Shorthand.

Arithmetic Series ::

An Arithmetic Series is a series of numbers in which each term increases by a constant amount.

How to find the sum of the Arithmetic Sequence or Series for the given Series ::

When the series contains a large amount of numbers, its impractical to add manually. You can quickly find the sum of any arithmetic sequence by multiplying the average of the first and last term by the number of terms in the sequence.

That is given by Sn = n(a1 + an)2 Where n = number of terms, a1 = first term, an = last term

Here Last term is given by an = a1 + n-1d where d = common difference

Now given Arithmetic Series is 

2, 5, 8, 11,...

Here a1 = 2,  d = 3, n = 36 

Now, $$\begin{gathered} an= a1 + n - 1d \\ a36= 2 + 36 - 13 = 105 + 2 = 107 \end{gathered}$$

Now, Sum to 36 terms is given by

S36 = 36(2 + 107)2 = 36 x 1092 = 39242 = 1962

Therefore, Sum to 36 terms of the series 2, 5, 8, 11,... is 1962.

The given number series is 720, 732, 708, 742, 696

720

720 + 12 = 732

732 - 24 = 708

708 + 36 = 744 (Not 742)

744 - 48 = 696

Hence, the odd man in the given number series is 742.

The given series is 8, 14, 24, 60, 180

8

8 x 1.5 = 12 (NOT 14)

12 x 2 = 24

24 x 2.5 = 60

60 x 3 = 180

Hence, the odd man in the given series is 12.

Here the given number series  3, 10.5, 36.75, 128.625, ? follows a pattern that

3

3 x 3.5 = 10.5

10.5 x 3.5 = 36.75

36.75 x 3.5 = 128.625

128.625 x 3.5 = 450.187

Hence the next number in the given number series is 450.187.