Answer

Verified

429.3k+ views

**Hint:**In this problem we have to find the value of common difference \[d\] by using given conditions. They gave the initial value \[a\], total number of elements \[n\] and \[{n^{th}}\] term of the arithmetic progression. By using the relations in the arithmetic progression we are going to solve this problem.

**Formula used:**

We know that, nth term of an arithmetic progression with the initial term as \[a\] and \[d\] be the common difference, is

\[{a_n} = a + (n - 1)d\]

Here, the given information is a series of an arithmetic progression. So, we will apply the values in the above formula.

Then we can find the value for \[d\].

**Complete step by step answer:**

It is given that; \[a = 3.5;\,{\text{ }}n = 105;{\text{ }}{a_n} = 3.5\]

It means the series is in arithmetic progression. So, the initial term is \[a = 3.5\], the value of n is \[ 105\] and the nth term is \[{a_n} = 3.5\].

We have to find the value of the common difference that is \[d\].

We know that, nth term of an arithmetic progression with the initial term as \[a\] and \[d\] be the common difference, is

\[{a_n} = a + (n - 1)d\]

Now, substitute the value in the above formula we get,

\[a = 3.5;\,{\text{ }}n = 105;{\text{ }}{a_n} = 3.5\]

\[ \Rightarrow {a_{105}} = 3.5 + (105 - 1)d\]

Let us substituting for \[{a_{105}} = 3.5\] and Simplifying we get,

\[ \Rightarrow 3.5 = 3.5 + (105 - 1)d\]

Simplifying we get,

\[ \Rightarrow d = 0\]

**$\therefore $ The value of \[d\] is \[0\].**

**Note:**

A progression is a special type of sequence for which it is possible to obtain a formula for the nth term. The Arithmetic Progression is the most commonly used sequence in maths with easy to understand formulas. Let’s have a look at its three different types of definitions.

Definition 1: A mathematical sequence in which the difference between two consecutive terms is always a constant and it is abbreviated as AP.

Definition 2: An arithmetic sequence or progression is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is obtained by adding a fixed number to the first one.

Recently Updated Pages

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

Advantages and disadvantages of science

Trending doubts

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

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

10 examples of evaporation in daily life with explanations

Difference Between Plant Cell and Animal Cell

Write a letter to the principal requesting him to grant class 10 english CBSE

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