## Arithmetic, geometric, and harmonic progressions

**Elements**

*a*_{1} = value of the first term

*a*_{m} = value of any term after the first term but before the last term

*a _{n}* = value of the last term

*n*= total number of terms

*m*=

*m*

^{th}term after the first but before

*n*

^{th}

*d*= common difference of arithmetic progression

*r*= common ratio of geometric progression

*S*= sum of the 1

^{st}

*n*terms