How to find the first four terms of a sequence?

The first four terms of the Arithmetic progression is a, a + d, a + 2d and a + 3d where a is the first term and d is the common difference. For any other sequence, u_n, its first four terms are u₁, u₂, u₃, and u₄.

What is Sequence?

An ordered list of numbers is called a sequence. Each number of the sequence is called a term. A sequence is denoted as, a₁, a₂, a₃, a₄,…..a_n. A finite sequence consists of a finite list of numbers such as for example { 2, 4, 8, 16, 32} is a finite sequence whereas an infinite sequence consists of an infinite list of numbers such as for example  { 3, 7, 11, 15,…}. The three dots represent that the sequence goes on to infinity.

How to Find first four terms of a sequence?

For any sequence un, we can just replace the value of n = 1, 2, 3, and 4; in the given sequence to find the first four terms.

Example: Find the first four terms of sequence u_n = 2^n-1/3.

Solution:

Given: u_n = 2^n-1/3

Put n = 1, 2, 3, and 4.

u₁ = 2^1-1/3 = 2⁰/3 = 1/3

u₂ = 2^2-1/3 = 2¹/3 = 2/3

u₃ = 2^3-1/3 = 2²/3 = 4/3

u₄ = 2^4-1/3 = 2³/3 = 8/3

Thus, First four terms of sequence u_n are {1/3, 2/3, 4/3, 8/3}.

For A.P.

The formula for the n^th term of an A.P. is:

a_n = a + d(n – 1) 

Or, the First four terms can also be easily found out with the help of the arithmetic sequence if the first term and the common difference are known i.e.,

A.P. = a, a + d, a + 2d, a + 3d, a +4d, . . .

Sample Questions for finding First Four Terms

Question 1: a_n = 5n + 3, Find the first four terms. 

Solution: 

To find the first four terms of the above sequence, find a₁, a₂, a₃, a₄, a_5,i.e; n= 1, 2, 3, 4 as the first term is given.

• a₁ = 5(1) + 3 = 5 + 3 = 8
• a₂ = 5(2) + 3 = 10 + 3 = 13
• a₃ = 5(3) + 3 = 15 + 3 = 18
• a₄ = 5(4) + 3 = 20 + 3 = 23

Therefore, the first four terms of a sequence are {8, 13, 18, 23}

Question 2:  a_n = 2ⁿ/2, Find the first four terms.

Solution:

To find the first four terms of the above sequence, find a₁, a₂, a₃, a₄, a_5,i.e; n= 1, 2, 3, 4 as the first term is given.

• a₁ = 2¹/2 = 1
• a₂ = 2²/2 = 4/2 = 2
• a₃ = 2³/2 = 8/2 = 4
• a₄ = 2⁴/2 = 16/2 = 8

Therefore, the first four terms of a sequence are {1, 2, 4, 8}

Question 3: Find the first four terms of an A.P. when a₁ = 10, d = 5.

Solution:

a₁ = 10 (first term)

d = 5 (common difference)

As discussed above, the arithmetic sequence is defined as,

a_n = a + (n – 1)d

Where a is the first term and d is the constant

so here, a = 10 and d = 5

• a₂ = 10 + 5(2 – 1) = 10 + 5(1) = 15
• a₃ = 10 + 5(3 – 1) = 10 + 5(2) = 10 + 10 = 20
• a₄ = 10 + 5(4 – 1) = 10 + 5(3) = 10 + 15= 25