What is the sum of the first (5) terms of the arithmetic progression (7,15,23,31,\ldots)?
Answer and explanation
Correct answer: 115
The governing concept is the sum of a finite arithmetic progression. The first term is a=7 and the common difference is d=15-7=8. The fifth term is a_5=a+(5-1)d=7+4(8)=39. Therefore the first five terms are 7, 15, 23, 31 and 39, whose sum is 7+15+23+31+39=115. Equivalently, S_n=n/2[2a+(n-1)d]=5/2[14+32]=5/2(46)=115. Thus option C is correct. The other choices result from incomplete addition or an incorrect fifth term; none equals the verified sum by either method.
Frequently asked questions
What is the correct answer to this question?
115
Why is this the correct answer?
The governing concept is the sum of a finite arithmetic progression. The first term is a=7 and the common difference is d=15-7=8. The fifth term is a_5=a+(5-1)d=7+4(8)=39. Therefore the first five terms are 7, 15, 23, 31 and 39, whose sum is 7+15+23+31+39=115. Equivalently, S_n=n/2[2a+(n-1)d]=5/2[14+32]=5/2(46)=115. Thus option C is correct. The other choices result from incomplete addition or an incorrect fifth term; none equals the verified sum by either method.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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