Lucky number 7
Algebra
Level
2
An arithmetic progression has 13 terms. The sum of the odd terms (first, third, fifth, etc) is 98. What is the value of the seventh term?
Based on alternative solution to previous problem
The answer is 14.
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1 solution
The odd terms of an arithmetic progression are themselves an arithmetic progression. We cannot work out the first term and common difference, but we can pair up most of the seven numbers that make up the odd terms.
Let the first, third, fifth, ..., thirteenth terms be:
a, a+d, a+2d, a+3d, a+4d, a+5d, a+6d
Find 3 pairs which sum to 2a+6d, which is twice the middle term a+3d. So 7(a+3d) = 98
So a+3d (which is the seventh term of the original sequence) is 14.