Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

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

  • Last Updated : 05 Aug, 2021

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.

Hey! Looking for some great resources suitable for young ones? You've come to the right place. Check out our self-paced courses designed for students of grades I-XII

Start with topics like Python, HTML, ML, and learn to make some games and apps all with the help of our expertly designed content! So students worry no more, because GeeksforGeeks School is now here!

 



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 nth term in an AP series.

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

 T(n) = a + (n – 1) × d  

 where, 

a = first term,

 d = common difference

What are the first four terms of the A.P. 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

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

My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!