Arithmetic Sequence Formula

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Arithmetic sequence is the sequence of numbers where every succeeding number follows a particular rule. In

an arithmetic sequence, the difference between any two numbers is constant hence it is called the common

difference of the terms. Arithmetic sequence formula is the formula which uses the first term and the common

difference to get the sequence.


Example 1: Find the 12th term of the sequence: 1, 5, 9, 13……


Given sequence is arithmetic sequence because,

5 - 1 = 4 or 9 - 5 = 4

Common difference between any two consecutive numbers is 4.

So first term, a1 = 1

Common difference, d = 4

So nth term = a + (n-1)d

12th term -> n = 12

So, 12th term = 1 + (12-1)*4

12th term = 1 + (11* 4)->12th term = 1 + 44 = 45
 
Example 2: For the above sequence:1, 5, 9, 13…… find the sum of the sequence till the 12th term.

Sum of certain number of terms of an Arithmetic sequence = Sn = n/2 * (a1 + an)

Given, first term, a1 = 1

Last term, a12= 45 (from the above answer)

n = 12 terms

So sum -> Sn = n/2 * (a1 + an)

S12 = 12/2 * (1 + 45)

S12 = 6 * (46)

S12 = 276

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