Arithmetic progression (A.P.) is a sequence of numbers which is generated by adding a common difference (d) from the previous number.

**Nth term of Arithmetic progression**

a_{n} = a_{1} + d(n-1)
_{1}a is not available a modified formula can be used.

a_{n} = a_{m} + d(n-m)

Where:

a_{n} = The nth term

a_{m} = The mth term

a_{1} = The 1st term

d = The common difference (a_{n} - a_{n-1})

n = number of terms

m = number of terms up to a_{m} where m < n

If aa

a

a

d = The common difference (a

n = number of terms

m = number of terms up to a

a

**Summation of Arithmetic progression**

\( s =\frac{n}{2}(a_1 +a_2)\)

But: \(a_n = a_1 +d(n-1)\)

Thus:

\(S = \frac{n}{2} [a_1 +a_1 +d(n-1)]\)

\(S = \frac{n}{2} [2a_1 +d(n-1)]\)