How Many Terms of the AP : 9, 17, 25, . . . must be taken to Give a Sum of 636?

Total Terms of AP 9, 17, 25, . . . whose Sum is 636

As discussed above, 12 is the total number of terms of the AP 9, 17, 25, . . . to give a sum of 636. To solve the question, it is important to understand what AP is. AP in mathematics stands for Arithmetic Progression. 

• AP is a set of numbers where the difference between each term from its predecessor is fixed throughout the entire sequence.
• The common difference of that arithmetic progression is the constant difference. 
• In other words, A list of numbers is an arithmetic progression if every term, with the exception of the first, is obtained by adding a fixed number to the term before it.
• This fixed number is referred to as the common difference of an AP. The common difference can be positive, negative, or zero.
• It is represented by ‘d’ in the formula of AP.

Summary:

How Many Terms of the AP 9, 17, 25, . . . must be taken to Give a Sum of 636?

The total terms of AP 9, 17, 25, . . . that must be taken to give a sum of 636 is 12. It can be determined by putting the given values in the formula to calculate the sum of first ‘n’ terms of an AP i.e. S_n = n/2 [2a + (n - 1) d] or S_n = n/2 [a + 1].