An arithmetic progression is simply a progression with a common difference among consecutive terms.
- <em>The sum of multiplies of 6 between 8 and 70 is 390</em>
- <em>The sum of multiplies of 5 between 12 and 92 is 840</em>
- <em>The sum of multiplies of 3 between 1 and 50 is 408</em>
- <em>The sum of multiplies of 11 between 10 and 122 is 726</em>
- <em>The sum of multiplies of 9 between 25 and 100 is 567</em>
- <em>The sum of the first 20 terms is 630</em>
- <em>The sum of the first 15 terms is 480</em>
- <em>The sum of the first 32 terms is 3136</em>
- <em>The sum of the first 27 terms is -486</em>
- <em>The sum of the first 51 terms is 2193</em>
<em />
<u>(a) Sum of multiples of 6, between 8 and 70</u>
There are 10 multiples of 6 between 8 and 70, and the first of them is 12.
This means that:
The sum of n terms of an AP is:
Substitute known values
<u>(b) Multiples of 5 between 12 and 92</u>
There are 16 multiples of 5 between 12 and 92, and the first of them is 15.
This means that:
The sum of n terms of an AP is:
Substitute known values
<u>(c) Multiples of 3 between 1 and 50</u>
There are 16 multiples of 3 between 1 and 50, and the first of them is 3.
This means that:
The sum of n terms of an AP is:
Substitute known values
<u>(d) Multiples of 11 between 10 and 122</u>
There are 11 multiples of 11 between 10 and 122, and the first of them is 11.
This means that:
The sum of n terms of an AP is:
Substitute known values
<u />
<u>(e) Multiples of 9 between 25 and 100</u>
There are 9 multiples of 9 between 25 and 100, and the first of them is 27.
This means that:
The sum of n terms of an AP is:
Substitute known values
<u>(f) Sum of first 20 terms</u>
The given parameters are:
The sum of n terms of an AP is:
Substitute known values
<u>(f) Sum of first 15 terms</u>
The given parameters are:
The sum of n terms of an AP is:
Substitute known values
<u>(g) Sum of first 32 terms</u>
The given parameters are:
The sum of n terms of an AP is:
Substitute known values
<u>(g) Sum of first 27 terms</u>
The given parameters are:
The sum of n terms of an AP is:
Substitute known values
<u>(h) Sum of first 51 terms</u>
The given parameters are:
The sum of n terms of an AP is:
Substitute known values
Read more about arithmetic progressions at: