Answer

Verified

475.5k+ views

Hint- In order to solve such a question consider 0 to be a term, then with the help of formula of nth term of an A.P. find the value of n or the term number. If the value of n be an integer then our consideration will be right otherwise wrong.

Complete step-by-step solution -

Given A.P. is $40,37,34,31,....$

For a general A.P. with $a$ as first term and $d$ be its common difference.

Nth term of the general A.P. is

${a_n} = a + \left( {n - 1} \right)d$

For the given A.P.

$

a = 40 \\

d = {a_2} - {a_1} = 37 - 40 = - 3 \\

$

Let us consider 0 is the nth term of the A.P.

$ \Rightarrow {a_n} = 0$

Also we have

$

\Rightarrow {a_n} = a + \left( {n - 1} \right)d = 0 \\

\Rightarrow 40 + \left( {n - 1} \right)\left( { - 3} \right) = 0 \\

$

Solving the equation for the value of n

\[

\Rightarrow 40 + \left( {n - 1} \right)\left( { - 3} \right) = 0 \\

\Rightarrow \left( {n - 1} \right)\left( { - 3} \right) = - 40 \\

\Rightarrow \left( {n - 1} \right)\left( 3 \right) = 40 \\

\Rightarrow \left( {n - 1} \right) = \dfrac{{40}}{3} \\

\Rightarrow n = \dfrac{{40}}{3} + 1 \\

\Rightarrow n = \dfrac{{40 + 3}}{3} \\

\Rightarrow n = \dfrac{{43}}{3} \\

\]

Since the term number in an A.P. cannot be a decimal number. It can only be an integer. So our consideration is false.

Hence, 0 is not a term of the given A.P.

Note- An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant. For example, the sequence 2, 4, 6, 8 ... is an arithmetic progression with common difference 2. Always remember the formula of the nth term of an A.P. and the sum of an A.P.

Complete step-by-step solution -

Given A.P. is $40,37,34,31,....$

For a general A.P. with $a$ as first term and $d$ be its common difference.

Nth term of the general A.P. is

${a_n} = a + \left( {n - 1} \right)d$

For the given A.P.

$

a = 40 \\

d = {a_2} - {a_1} = 37 - 40 = - 3 \\

$

Let us consider 0 is the nth term of the A.P.

$ \Rightarrow {a_n} = 0$

Also we have

$

\Rightarrow {a_n} = a + \left( {n - 1} \right)d = 0 \\

\Rightarrow 40 + \left( {n - 1} \right)\left( { - 3} \right) = 0 \\

$

Solving the equation for the value of n

\[

\Rightarrow 40 + \left( {n - 1} \right)\left( { - 3} \right) = 0 \\

\Rightarrow \left( {n - 1} \right)\left( { - 3} \right) = - 40 \\

\Rightarrow \left( {n - 1} \right)\left( 3 \right) = 40 \\

\Rightarrow \left( {n - 1} \right) = \dfrac{{40}}{3} \\

\Rightarrow n = \dfrac{{40}}{3} + 1 \\

\Rightarrow n = \dfrac{{40 + 3}}{3} \\

\Rightarrow n = \dfrac{{43}}{3} \\

\]

Since the term number in an A.P. cannot be a decimal number. It can only be an integer. So our consideration is false.

Hence, 0 is not a term of the given A.P.

Note- An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant. For example, the sequence 2, 4, 6, 8 ... is an arithmetic progression with common difference 2. Always remember the formula of the nth term of an A.P. and the sum of an A.P.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths