Algebraic Sequence Formula

Before learning the algebraic sequence formula, let us recall what is an algebraic sequence. An algebraic sequence, also known as an arithmetic sequence, is a type of sequence in which the difference between every consecutive term is the same. The difference is known as a common difference. To define an algebraic sequence we should know the first term of the sequence and the common difference. The algebraic sequence formula is used to define any term in the sequence.

What is Algebraic Sequence Formula?

The algebraic sequence formula is nothing but the formula that is used to find the n^th term of an arithmetic sequence given its first term and the common difference. It can be expressed as,

\(a_n\) = a + d(n-1)

where,

• a_n = n^th term of the algebraic sequence
• a = first term
• d = common difference

Let us see the applications of the algebraic sequence formula in the solved examples section below.

Examples Using Algebraic Sequence Formula

Example 1: Find the 56th term of an algebraic sequence 7,11,15,19…

Solution: 

To find: 56th term of an algebraic sequence
Given: a = 7
d = (11-7) = (15-11) = (19-15) = 4
n = 56
Now, using algebraic sequence formula,
a_n = a + d(n-1)
a₅₆ = 7 + 4(56-1)
=7 + (4)(55)
=7 + 220
=227 

Answer: 56th term of the given algebraic sequence is 227.

Example 2: Find which term is zero in the algebraic sequence 301, 294, 287, 280…

Solution: 

To find: Which term is zero that is n.

Given,
a = 301
d = (294 – 301) = (287 – 294) = (280 – 287) = (-7)
a_n = 0

Using algebraic sequence formula,
a_n = a + d(n-1)
0  = 301 + (-7) (n-1)
(-301)  = (-7) (n-1)
(-301) / (-7) = n-1
n-1 =43
n = 43 + 1
n = 44

Answer: 44th term of the given algebraic sequence is zero.