Write the first four term of the AP when the first term a =10 and common difference d =10 are given?

First four terms of the AP when the first term a = 10 and common difference d = 10 are 10, 20, 30 and 40. The first four terms of A.P. when the first term is a and common difference d is given are a, a + d, a + 2d and a + 3d. The nth of A.P. can be calculated by the nth term formula a_n = a + (n-1)d, where an is the nth term, a is the first term, d is the common difference and n is the term which we want to find.

So, by using the formula

a_n = a + (n-1)d,

a₁ = a + (1-1)d = a,

a₂ = a + (2-1)d = a + d,

a₃ = a + (3-1)d = a + 2d,

a₄ = a + (4-1)d = a + 3d.

Hence, the first four term of A.P. is a , a + d , a + 2d and a + 3d. For given A.P. whose first term a = 10 and common difference d = 10 , the first four terms are 10 , 20 , 30 and 40.

What is Arithmetic Progression?

Arithmetic Progression, (AP) is a series of numbers in which the difference between any two consecutive numbers is a constant value. Common Difference of an Arithmetic Progression is the constant value difference between the next term and the previous term of a progression. It is denoted by d in mathematics. The common difference of an Arithmetic Progression can be positive, negative, or zero.

For a series of numbers in Arithmetic Progression, if multiple pairs are formed of consecutive numbers or numbers at particular intervals and the difference is calculated between the elements of each pair, we will see that all pairs are having the same difference. 

An example of AP series is 4, 8, 12, 16, 20, 24, … Here if pairs of consecutive numbers are formed let’s say of (8, 12) and (20, 24), and find out the common difference between the elements of the pairs, which is 12- 8= 4 and 24- 20= 4. So both share a common difference.

First Term and Common Difference in Arithmetic Progression

The first term in the Arithmetic progression is represented as “a”, and the common difference is represented as “d”. A common difference in A.P. is the difference between two consecutive terms. Therefore, if the first term is denoted as “a”, the next term becomes “a+ d”,

a + (a + d) + (a + 2d) + (a + 3d) + … + {a + (n – 1) × d}

where n = 1, 2, 3, 4, . . . 

Here, n denotes the n^th term in an AP series.

So the value of an n^th term of a series in Arithmetic Progression can be found out by using the formula,

T(n) = a + (n – 1) × d

 where,

• a is First Term
• d is Common Difference

What are the first four terms of the AP when First term, a= 10, Common Difference, d= 10.

Now, use the above formula, a+ (n-1)d to find out the values of the first four terms of an AP series where the first term is a = 10 and common difference d = 10, which turns out to be,

a₁ = 10

a₂ = a+ (n-1)d= 10 + (2 – 1) × 10 = 20

Or

a + d = 10 + 10 = 20

a₂ = 20

a₃ = a+ (n-1)d= 10 + (3 – 1) × 10 = 30

Or  

a + 2d = 10 + 2×10 = 30

a₃ = 30

a₄ =  a+ (n-1)d = 10 + (4 – 1) × 10 = 40

Or  

a + 3d = 10 + 3×10 = 40

a₄ = 40

Now first four terms of the required AP are, 10, 20, 30, and 40.

Similar Questions

Question 1: Find the first four terms of the A.P. when the first term is 2 and the common difference is 5.

Solution:

First-term, a= 2

Common difference= 5

A.P. First four terms= a, a+ d, a+ 2d, a+ 3d

a₁= 2

a₂= 2+ 5= 7

a₂= 7

a₃= 2+ 2× 5= 12

a₃= 12

a₄= 2+ 3× 5= 17

a₄= 17

Question 2: Find the first four terms of the A.P. when the first term is 5 and the common difference is 3.

Solution:

First-term, a= 5

Common difference= 3

A.P. First four terms= a, a+ d, a+ 2d, a+ 3d

a₁= 5

a₂= 5+ 3= 8

a₂= 8

a₃= 5+ 2× 3= 11

a₃= 11

a₄= 5+ 3× 3= 14

a₄= 14

Question 3: Find the first five terms of the A.P. when the first term is 10 and the common difference is 20.

Solution:

First-term, a= 10

Common difference= 20

A.P. First four terms= a, a+ d, a+ 2d, a+ 3d, a+ 4d

a₁= 10

a₂= 10+ 20= 30

a₂= 30

a₃= 10 + 2× 20= 50

a₃= 50

a₄= 10+ 3× 20= 70

a₄= 70

a₅= 10+ 4× 20= 90

a₅= 90