What is a_{1}+a_{5}-a_{10}-a_{15}-a_{20}-a_{25}+a_{30}+a_{34} equal to ?
Consider the following for the next two (02) items that follow : Let a_1, a_2, a_3 \dots be in AP such that a_{1}+a_{5}+a_{10}+a_{15}+a_{20}+a_{25}+a_{30}+a_{34}=300.
- A. 0 ✓
- B. 25
- C. 125
- D. 250
Correct Answer: A. 0
Explanation
In an AP, the sum of terms equidistant from the ends is constant. So, a_1 + a_{34} = a_5 + a_{30} = a_{10} + a_{25} = a_{15} + a_{20} = S. The given equation 4S = 300 gives S = 75. The required expression is (a_1+a_{34}) + (a_5+a_{30}) - (a_{10}+a_{25}) - (a_{15}+a_{20}) = S + S - S - S = 0.
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