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.

Customer ratio of Milk and Water is given by

Milk          ::        Water

  6.4                         0

         81 + 38 =6411

 6411                      6410 - 6411

=> Milk : Water = 110 : 11 = 10 : 1

Therefore, the proportionate of Water to Milk for Customer is 1 : 10

About 150 - 200 species of plant, insect, bird and mammal become extinct every day or 24 hrs.

This is not an accurate but an estimation by U.N. Convention on Biological Diversity and Global Extinction Rates. It is also said that current extinctions were 'up to 100 times higher than the background rate.'

Given nuber series is 15, 30, ? , 40, 8, 48 

Here the number series follows a pattern that

15

15 x 2 = 30

30 ÷ 3 = 10

10 x 4 = 40

40 ÷ 5 = 8

8 x 6 = 48

Hence, the missing number in the series is 10.

We know thatThe Difference between Compound Interest and Simple Interest for n years at R rate of interest is given by C.In - S.In = PR100n

Here n = 2 years, R = 20%, C.I - S.I = 56

$$\begin{gathered} 56 = P201002 \\ => P = 56 x 52 \\ => P = 56 x 25 \\ => P = Rs. 1400 \end{gathered}$$

Proteins are long chains of Amino acids. That is in brief, Amino acids are the monomers of Proteins. Amino acids are compounds which contain both an amino group and a carboxylic group. Proteins are made up of 20 essential amino acids.

Monomer means a small molecule of an organic substance i.e, building block in general.

Asbestos can cause

•  Lungs

• Gastrointestinal tract  types of Cancer.

Benzene can cause

• Leukemia

• Hodgkin's lymphoma types of Cancer.

Cadmium can cause

• Prostate type of Cancer.

Let Speed of boat in still water = b

Let Speed of still water = w

Then we know that,

Speed of Upstream = U = boat - water

Speed of Downstream = D = boat + water

Given, U + D = 82

b - w + b + w = 82

2b = 82

=> b = 41 kmph

From the given data,

41 - w = 105/3 = 35

w = 6 kmph

Now,

b + w = 126/t

=> 41 + 6 = 126/t

=> t = 126/47  = 2.68 hrs.