Sequences & Series
Infinite Geometric Series
Grade 11
Question:
<p>(a) Consider an infinite geometric series with first term 'a' and common ratio r. If the sum is 4 and the second term is 3/4, then:</p>
<p>(A) <i>a</i> = ?, <i>r</i> = ?</p>
<p>(B) <i>a</i> = 2, <i>r</i> = ?</p>
<p>(C) <i>a</i> = ?, <i>r</i> = ?</p>
<p>(D) <i>a</i> = 3, <i>r</i> = ?</p>
Step-by-Step Solution
Key Concept: Use the infinite G.P. sum formula and the term formula to find both parameters.
<p>Given: Sum = 4, second term = ar = 3/4</p><p>From sum formula: \(S = \frac{a}{1-r} = 4\)</p><p>From second term: \(ar = \frac{3}{4}\)</p><p>Solving: <i>a</i> = 2, <i>r</i> = 3/8</p>
Correct Answer: B