The sum of n-numbers of an arithmetic progression is given by
S=nx*dn(n-1)/2
where x is the first number and d is the constant increment.
example:
sum of first 10 positive odd numbers:10*1+2*10*9/2=10+90=100
sum of first 10 multiples of 7 starting at 7: 10*7+7*10*9/2=70+315=385
remember:
For a descending AP the constant difference is negative.
Sequence of Numbers
A sequence is a set of numbers that follow a fixed pattern.The fixed pattern can be expressed by an equation or by a property.
Example:
A set of consecutive integers: 1,2,3,4,5(Fixed gap)
A set of consecutive even numbers:4,6,8,10,12 (Fixed gap)
A set of consecutive prime: 2,3,5,7,11(Fixed gap)
A set of consecutive power of 2:4,8,16,32,64(Fixed gap)
Remember:
A sequence can be in ascending or desceding order.
S=nx*dn(n-1)/2
where x is the first number and d is the constant increment.
example:
sum of first 10 positive odd numbers:10*1+2*10*9/2=10+90=100
sum of first 10 multiples of 7 starting at 7: 10*7+7*10*9/2=70+315=385
remember:
For a descending AP the constant difference is negative.
Sequence of Numbers
A sequence is a set of numbers that follow a fixed pattern.The fixed pattern can be expressed by an equation or by a property.
Example:
A set of consecutive integers: 1,2,3,4,5(Fixed gap)
A set of consecutive even numbers:4,6,8,10,12 (Fixed gap)
A set of consecutive prime: 2,3,5,7,11(Fixed gap)
A set of consecutive power of 2:4,8,16,32,64(Fixed gap)
Remember:
A sequence can be in ascending or desceding order.