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, un, 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,…..an. 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 un = 2n-1/3.
Solution:
Given: un = 2n-1/3
Put n = 1, 2, 3, and 4.
u1 = 21-1/3 = 20/3 = 1/3
u2 = 22-1/3 = 21/3 = 2/3
u3 = 23-1/3 = 22/3 = 4/3
u4 = 24-1/3 = 23/3 = 8/3
Thus, First four terms of sequence un are {1/3, 2/3, 4/3, 8/3}.
For A.P.
The formula for the nth term of an A.P. is:
an = 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: an = 5n + 3, Find the first four terms.
Solution:
To find the first four terms of the above sequence, find a1, a2, a3, a4, a5,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: an = 2n/2, Find the first four terms.
Solution:
To find the first four terms of the above sequence, find a1, a2, a3, a4, a5,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,
an = 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
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