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Which term of the progression 4, 9, 14, 19 is 109?

  • Difficulty Level : Hard
  • Last Updated : 05 Aug, 2021

A number System is portrayed as a course of action of writing to represent the numbers. It is the numerical documentation for addressing amounts of a given set by using digits or symbols in a consistent manner. It gives an exceptional portrayal of each number and addresses the math and logarithmic construction of the figures. It additionally permits us to operate arithmetic operations like addition, subtraction, and division. The number the numeral addresses is called its value. 

Arithmetic

It is the branch of mathematics that deals with addition, subtraction, multiplication, and division on numbers. the common operation performed on numbers are addition, multiplication, subtraction, and division. It is a very integral and important part of number theory.

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Progression



Progression can be called a number in a series. It can be called a sequence in which a term is related to the previous term by any common law. Some examples of Progressions are Arithmetic progression, Geometric progression, Harmonic progression.

Arithmetic progression: sequence of numbers where the difference of any two successive numbers of the sequence is the same.

Geometric progression: sequence of numbers where the quotient of any two successive numbers of the sequence is the same.

Harmonic progression: sequence of numbers where their reciprocals form an arithmetic progression.

Arithmetic Progression

An arithmetic progression or sequence is a series/sequence of numbers such that the common difference between the consecutive terms remains constant i.e; each term differs by the previous term ( if exits) by a constant value.

Formula for the nth term of the Arithmetic Progression:

an= a + (n – 1)d.



where;

a= first term

d=common difference

Which term of the progression 4,9, 14, 19 is 109 

a= 4, d= 5

The formula to find the nth term of the Arithmetic Progression:

an= a + (n – 1) d.

here, 

an= 109, a= 4, and d= 5 and we need to find the n.

Therefore: 

109=4+(n-1)×5

=105/5=(n-1)

n=22.

Hence, 109 is the 22nd term of the Arithmetic Progression.

Similar Questions

Question 1: Write the A.P. when the first term is 20 and the common difference is 2.

Solution:

Given: a = 20  and d = 2

Let us consider, the Arithmetic Progression series be a1, a2, a3, a4, a5

a1 = a = 20

a2 = a1 + d = 20 + 2 = 22

a3 = a2 + d = 22 + 2 = 24



a4 = a3 + d = 24+ 2 = 26

And so on…

Therefore, the A.P. is 20, 22, 24,26…

Question 2:  Find the 13th term of an AP if the first term is 6 and the common difference is 3.

Solution:

a=6, d=3

The formula to find the nth term of the Arithmetic Progression:

an= a + (n – 1)d.

here,

n=13,  a=6, and d=3 and we need to find the 13th term.

Therefore:

an= 6 + ( 13- 1 )3

an= 42

Hence, the 13th term is 42.

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