Question

How many terms of the arithmetic progression 12, 18, 24 must be taken so that their sum is 210?

Answer 1

❒ Given :-

• ➊ First term = 12
• ➋ Common Difference = 18 - 12 = 6
• ➌ Sum of terms = 210

❒ To Find :-

• ➊ Number of terms must be taken so that their sum is 210

❒ Solution :-

By using Sn Formula

$\large \longmapsto \underline{ \boxed{ \bf \red{S_n = \frac{1}{2} \bigg[2a + (n - 1)d \bigg]}}}$

Here :-

• Sn = Sum of all terms
• a = First term
• n = number of terms
• d = common difference

★ Substitute values in formula

$:\implies \tt210 = \frac{1}{2} \bigg[2 \times 12 + (n - 1)6 \bigg]$

$:\implies \tt210 \times 2 = \bigg[24+ (n - 1)6 \bigg]$

$:\implies \tt420 = \bigg[24+ (n - 1)6 \bigg]$

$:\implies \tt420 - 24 =(n - 1)6$

$:\implies \tt396 =(n - 1)6$

$:\implies \tt \frac{396}{6} =n - 1$

$:\implies \tt66 =n - 1$

$:\implies \tt n = 66 + 1$

$:\implies \boxed{ \tt n =67}$

Answer 2

Answer:

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Step-by-step explanation:

Chemistry has made a profound impact on the society. It is intimately linked

to the well-being of human kind. The rate of advancements in chemistry is so

high that curriculum developers continuously look for strategies to cope with

these advancements. Also, the students have to be inspired to be the future

leaders who would make fundamental contributions. The present textbook is

a sincere effort in this direction.

The structure of the textbook, presented in two parts, comprises of sixteen

Units. Although the titles of various Units indicate a sort of

compartmentalisation into physical, inorganic and organic chemistry, readers

will find that these sub-disciplines have been intermingled, at least to a certain

extent, to have a unified approach to the subject. The approach of presentation

of the subject matter discourages students from rote memorisation. The subject

has in fact, been organised around the laws and principles of chemistry. As

students master these laws and principles, they will soon get to the point

where they can predict much of what will come.

Efforts have been directed towards making the subject stimulating and

exciting by references to the historical developments and its usefulness to our

lives, wherever appropriate. The text is well illustrated with examples from

surrounding environment to facilitate grasping of the qualitative and

quantitative aspects of the concept easily. Physical data are given in SI units

throughout the book to make comparison of various properties easier. IUPAC

system of nomenclature has been followed along with the common system.

Structural formulae of chemical compounds showing functional/coordinating

groups in different colours are drawn using electronic system. Each Unit has

a good number of examples, as illustrations, with their solutions and some

intext questions, the answers of some of which are given at the end of the Unit.

The end of Unit exercises are designed to apply important principles and

provoke thinking process to solve them. Answers of some of these exercises

are given at the end of the book.

A variety of materials, e.g., biographical sketches of some scientists,

additional information related to a particular topic, etc., is given in boxes with

a deep yellow coloured bar. This boxed material with a 'deep yellow bar' is to

bring additional life to the topic. However, it is non-evaluative. The structures

of some of the more complex compounds incorporated in the book are for

understanding their chemistry. As their reproduction would lead to

memorisation, it is also a non-evaluative portion of the text.

The information part has been significantly reduced and, wherever possible,

it has been substantiated with facts. However, it is necessary for students to