About Algebraic Sequence Formula
Let us first define an algebraic sequence before understanding the algebraic sequence formula.
Algebraic Sequence Formula
Let us first define an algebraic sequence before understanding the algebraic sequence formula. The difference between each subsequent term in an algebraic series, also known as an arithmetic sequence, is the same. The distinction is referred to as a common difference. We need to know the initial term and the common difference to define an algebraic sequence. Any phrase in the sequence is defined using the algebraic sequence formula.
What is the formula for the algebraic sequence?
The algebraic sequence formula is the formula for determining the nth term of an arithmetic sequence given the initial term and common difference. It can be stated as follows:
an = a + (n-1)d
where an is the algebraic sequence's nth term
a = initial phrase
d = common distinction
In the solved examples section below, we'll look at how the algebraic sequence formula is used.
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Algebraic Sequence Formula Examples
Example 1: In an algebraic sequence of 7,11,15,19..., find the 56th term.
Solution: To find: An algebraic sequence's 56th term
Given: a = 7
d = (11-7) = (15-11) = (19-15) = 4
n = 56
Using the algebraic sequence formula, now
an = a + (n-1)d
a56 = 7 + 4(56-1)
=7 + (4)(55)
=7 + 220
=227
Example 2: Determine which term in the algebraic sequence 301, 294, 287, 280... is zero.
Solution: Determine which term is n and is zero.
It has given, a = 301, we have
d = (294 – 301) = (287 – 294) = (280 – 287) = (-7)
an = 0
Using the formula for algebraic sequence,
an = a + (n-1)d
0 = 301 + (n-1) (-7)
(-301) = (n-1) (-7)
(-301) / (-7) = n-1
n-1 =43
n = 43 + 1
n = 44
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