Sequences & Series
Arithmetic Progression
Grade 11
Question:
<p>Let <span class="math">a_1, a_2, a_3, \ldots, a_{49}</span> be in A.P. such that <span class="math">a_9 + a_{43} = 66</span>.</p><p>If <span class="math">\sum_{i=1}^{49} \frac{1}{a_i}</span> is to be calculated, then <span class="math">m</span> is equal to</p>
<p>(A) 33</p>
<p>(B) 66</p>
<p>(C) 68</p>
<p>(D) 34</p>
Step-by-Step Solution
Key Concept: In an A.P. with odd number of terms, equidistant terms sum to twice the middle term.
<p>For an A.P. with 49 terms, the middle term is \(a_{25}\).</p><p>By property of A.P.: \(a_9 + a_{43} = a_1 + a_{49} = 2a_{25} = 66\)</p><p>Therefore \(a_{25} = 33\)</p><p>∴ Answer is (A).</p>
Correct Answer: A