Answer
Verified
384.6k+ views
Hint:Use the formula for finding the nth term of an arithmetic progression when its first term (a) and common difference (d) are given, and then put the given data in that equation or formula, you will then get one equation and one variable. Just solve the equation for that variable you will get the required common difference.
nth term of an A.P. with “a” as its first term and “d” be its common difference is given as follows:
${{\text{T}}_n} = a + (n - 1)d$
Complete step by step solution:
To find “d”, let us first understand the meaning of all terms in the question.
The question is saying in an Arithmetic Progression (A.P.) if its first term and the fifteenth term is given $(a = 13,\;{\text{T}} = 55)$ then we have to find its common difference $(d)$, we will proceed in this problem with the arithmetic formula for the nth term, which is given as follows
${{\text{T}}_n} = a + (n - 1)d,\;where\;{{\text{T}}_n},\;a\;{\text{and}}\;d$ are nth term, first term and the common difference of the arithmetic series.
According to the question,
$
\Rightarrow 55 = 13 + (15 - 1)d \\
\Rightarrow 55 = 13 + 14d \\
\Rightarrow 14d = 55 - 13 \\
\Rightarrow 14d = 42 \\
\Rightarrow d = \dfrac{{42}}{{14}} \\
\Rightarrow d = 3 \\
$
Therefore the required common difference of the Arithmetic Progression, whose first term is $13$ and fifteenth term is $55$ is equals to $3$
Formula used: Arithmetic progression formula for nth term: ${{\text{T}}_n} = a + (n - 1)d$
Additional information: Nature of an A.P. depends upon its common difference that is A.P. is increasing or decreasing according to the common difference is positive or negative
Note: Common difference is the fixed number or constant number that is further added and added to a number to get an arithmetic progression of numbers. Common difference of an arithmetic progression can be achieved by subtracting any term of the arithmetic progression from its consecutive next term.
nth term of an A.P. with “a” as its first term and “d” be its common difference is given as follows:
${{\text{T}}_n} = a + (n - 1)d$
Complete step by step solution:
To find “d”, let us first understand the meaning of all terms in the question.
The question is saying in an Arithmetic Progression (A.P.) if its first term and the fifteenth term is given $(a = 13,\;{\text{T}} = 55)$ then we have to find its common difference $(d)$, we will proceed in this problem with the arithmetic formula for the nth term, which is given as follows
${{\text{T}}_n} = a + (n - 1)d,\;where\;{{\text{T}}_n},\;a\;{\text{and}}\;d$ are nth term, first term and the common difference of the arithmetic series.
According to the question,
$
\Rightarrow 55 = 13 + (15 - 1)d \\
\Rightarrow 55 = 13 + 14d \\
\Rightarrow 14d = 55 - 13 \\
\Rightarrow 14d = 42 \\
\Rightarrow d = \dfrac{{42}}{{14}} \\
\Rightarrow d = 3 \\
$
Therefore the required common difference of the Arithmetic Progression, whose first term is $13$ and fifteenth term is $55$ is equals to $3$
Formula used: Arithmetic progression formula for nth term: ${{\text{T}}_n} = a + (n - 1)d$
Additional information: Nature of an A.P. depends upon its common difference that is A.P. is increasing or decreasing according to the common difference is positive or negative
Note: Common difference is the fixed number or constant number that is further added and added to a number to get an arithmetic progression of numbers. Common difference of an arithmetic progression can be achieved by subtracting any term of the arithmetic progression from its consecutive next term.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Why Are Noble Gases NonReactive class 11 chemistry CBSE
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
At which age domestication of animals started A Neolithic class 11 social science CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
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
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE