Exams

Platypus is the animal that gives both milk and eggs.

The given number series 410, 409, 413, 404, ? , follows a pattern that 

410

$$\begin{gathered} 410 - 13 = 409 \\ 409 + 22 = 413 \\ 413 - 33 = 404 \\ 404 + 42 = 420 \end{gathered}$$

Hence, the next number in the given series is 420.

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.

C.I. when interest
compounded yearly=rs.[5000*(1+4/100)(1+1/2*4/100)]

= Rs. 5304.

C.I. when interest is
compounded half-yearly=rs.5000(1+2/100)^3

= Rs. 5306.04
Difference = Rs. (5306.04 - 5304) = Rs. 2.04

This is a quadratic equation. To find n we multiply the last terms in each bracket together (2 times -5) = -10

To find ‘a’ we multiply the first terms in each bracket together (3x times 2x) = 6x2, So a = 6.

Thus a - n = 16

To find k we multiply the first term in the first bracket by the second term in the second bracket and add the result to the product of the second term in the first bracket and the first term in the second. (-15x + 4x) = -11x. So k = -11

16 - 11 = 5