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The first and last terms of an A.P. are 28 and 31. If the sum of its terms is 236, then the number of terms will be?
8
11
6
5
8
Use the average value method: The sum of terms is equal to the number of terms multiplied by the average of the first and last terms. Here, 236/((28+31)/2)=236/29.5=8.
First term a = 28, Last term l = 31, Sum of terms SnтАЛ = 236
SnтАЛ=2nтАЛ(a+l)
Use the average value method: The sum of terms is equal to the number of terms multiplied by the average of the first and last terms. Here, 236/((28+31)/2)=236/29.5=8.
Students often mistake the sum formula SnтАЛ=(n/2)(2a+(nтИТ1)d) and waste time trying to find the common difference d, which is unnecessary when the last term is already given.
Identify known variables
We are given the first term a=28, the last term l=31, and the total sum SnтАЛ=236.
a=28,l=31,SnтАЛ=236
Apply the sum formula
The sum of an arithmetic progression can be represented as SnтАЛ=2nтАЛ(a+l), where n is the number of terms.
236=2nтАЛ(28+31)
Solve for n
Simplify the expression inside the parentheses: 28+31=59. Then, 236=2nтАЛ(59), which leads to n=59236├Ч2тАЛ.
n=59472тАЛ=8
A is correct because the calculation of the number of terms results in n=8.
This formula is a special case of the general sum formula; remembering that anтАЛ=l=a+(nтИТ1)d connects AP to linear sequences in competitive exams.
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