Different A.P.’s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.’s having at least 3 terms and at most 33 terms is ______.
Correct Answer: 53
Solution and Explanation
The correct answer is 53
\(d_1=\frac{199−100}{2}∉I\)
\(d_2=\frac{199−100}{3}=33\)
\(d_3=\frac{199−100}{4}∉I\)
\(d_n=\frac{199−100}{i+1}∈I\)
di= 33 + 11, 9
Sum of CD’s = 33 + 11 + 9
= 53
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Concepts Used:
Arithmetic Progression
Arithmetic Progression (AP) is a mathematical series in which the difference between any two subsequent numbers is a fixed value.
For example, the natural number sequence 1, 2, 3, 4, 5, 6,... is an AP because the difference between two consecutive terms (say 1 and 2) is equal to one (2 -1). Even when dealing with odd and even numbers, the common difference between two consecutive words will be equal to 2.
In simpler words, an arithmetic progression is a collection of integers where each term is resulted by adding a fixed number to the preceding term apart from the first term.
For eg:- 4,6,8,10,12,14,16
We can notice Arithmetic Progression in our day-to-day lives too, for eg:- the number of days in a week, stacking chairs, etc.
Read More: Sum of First N Terms of an AP