Write the first four terms of the AP where a = 10 and d = 10
Arithmetic is a branch of mathematics that deals with the common operations performed in numbers which include addition, subtraction, multiplication, and division. Arithmetic is considered an elementary part of number theory; the term arithmetic was used as a synonym for number theory until the beginning of the twentieth century.
Progression
Progression can be considered as a sequence of numbers, where each member is evaluated according to the previous member of the sequence. Generally, progression is of three basic types,
- Arithmetic progression (A sequence where the next term is ahead of the previous term by a certain real number known as common difference)
- Geometric progression (A sequence where each term except the first is evaluated by multiplying the previous term with a non-zero real number known as common ratio)
- Harmonic progression (A sequence of numbers whose reciprocal forms arithmetic progression)
Arithmetic Progression
Arithmetic Progression is a sequence where each term except the first is evaluated by adding a certain real number to the previous term, and that real number is called a common difference.
Ak = Ak-1 + d
Here, d is a common difference. Letβs denote the first element of the sequence as βaβ, common difference as βdβ, then, the element at nth term denoted by An is given by,
An = a + (n-1) Γ d
Write the first four terms of the AP where a = 10 and d = 10
Solution:
According to the problem statement a = 10 and d = 10
Putting n = 1
A1 = 10 + (1 β 1) Γ 10 = 10
Hence, the first element is 10
Putting n = 2
A2 = 10 + (2 β 1) Γ 10 = 20
Hence, the Second element is 20
Putting n = 3
A3 = 10 + (3 β 1) Γ 10 = 30
Hence, the third element is 30
Putting n = 4
A4 = 10 + (4 β 1) Γ 10 = 40
The fourth element is 40
Hence, the first four terms of the AP are 10, 20, 30, 40
Similar Problems
Question 1: Write the first four terms of the AP where a = 1 and d = 2.
Solution:
According to the problem statement a=1 and d=2
Putting n = 1
A1 = 1 + (1 β 1) Γ 2 = 1
Hence, the first element is 1
Putting n = 2
A2 = 1 + (2 β 1) Γ 2 = 3
Hence, the Second element is 3
Putting n = 3
A3 = 1 + (3 β 1) Γ 2 = 5
Hence, the third element is 30
Putting n = 4
A4 = 1 + (4 β 1) Γ 2 = 7
Hence, the fourth element is 7
Hence, the first four terms of the AP are 1, 3, 5, 7
Question 2: Write the first four terms of the AP where a = 2 and d = -2.
Solution:
According to the problem statement a = 2 and d = -2
Putting n = 1
A1 = 2 + (1 β 1) Γ (-2) = 2
Hence, the first element is 2
Putting n = 2
A2 = 2 + (2 β 1) Γ (-2) = 0
Hence, the Second element is 0
Putting n = 3
A3 = 2 + (3 β 1) Γ (-2) = -2
Hence, the third element is -2
Putting n = 4
A4 = 2 + (4 β 1) Γ (-2) = -4
Hence, the fourth element is -4
Hence, the first four terms of the AP are 2, 0, -2, -4
Question 3: Write the first four terms of the AP where a = 1 and d = 0.5.
Solution:
According to the problem statement a = 1 and d = 0.5
Putting n = 1
A1 = 1 + (1 β 1) Γ (0.5) = 1
Hence, the first element is 1
Putting n = 2
A2 = 1 + (2 β 1) Γ (0.5) = 1.5
Hence, the Second element is 1.5
Putting n = 3
A3 = 1+ (3 β 1) Γ (0.5) = 2
Hence, the third element is 2
Putting n = 4
A4 = 1 + (4 β 1) Γ (0.5) = 2.5
Hence, the fourth element is 2.5
Hence, the first four terms of the AP are 1, 1.5, 2, 2.5
Question 4: Write the first four terms of the AP where a=2 and d=10.
Solution:
According to the problem statement a = 2 and d = 10
Putting n = 1
A1 = 2 + (1 β 1) Γ (10) = 2
Hence, the first element is 2
Putting n = 2
A2 = 2 + (2 β 1) Γ (10) = 12
Hence, the Second element is 12
Putting n = 3
A3 = 2 + (3 β 1) Γ (10) = 22
Hence, the third element is 22
Putting n = 4
A4 = 2 + (4 β 1) Γ (10) = 32
Hence, the fourth element is 32
Hence, the first four terms of the AP are 2, 12, 22, 32
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