- Filtre optionnel - |
- Filtre optionnel - |
An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Example: 2,4,6,8,10….. Arithmetic Series : The sum of the numbers in a finite arithmetic progression is called as Arithmetic series. Example: 2+4+6+8+10….. nth term in the finite arithmetic series Suppose Arithmetic Series a1+a2+a3+…..an Then nth term an=a1+(n-1)d Where a1- First number of the series an- Nth Term of the series n- Total number of terms in the series d- Difference between two successive numbers Sum of the total numbers of the arithmetic series Sn=n/2*(2*a1+(n-1)*d) Where Sn – Sum of the total numbers of the series a1- First number of the series n- Total number of terms in the series d- Difference between two successive numbers Example: Find n and sum of the numbers in the following series 3 + 6 + 9 + 12 + x? Here a1=3, d=6-3=3, n=5 x= a1+(n-1)d = 3+(5-1)3 = 15 Sn=n/2*(2a1+(n-1)*d) Sn=5/2*(2*3+(5-1)3)=5/2*18 = 45 I hope the above formulae are helpful to solve your math problems Thanks |
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