Answer

Verified

339.9k+ 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.

Recently Updated Pages

The branch of science which deals with nature and natural class 10 physics CBSE

Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred

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

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Distinguish between the reserved forests and protected class 10 biology CBSE

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

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which of the following books is not written by Harshavardhana class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

In which states of India are mango showers common What class 9 social science CBSE

What Made Mr Keesing Allow Anne to Talk in Class class 10 english CBSE