<p>A geometric series, $G$, has common ratio $r$, $r\ne 1$, and an arithmetic series, $A$, has a non-zero first term $a$.</p>
<p>The first three terms of $G$ are equal to the seventh, third and first term of $A$ respectively.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Show that $2{{r}^{2}}-3r+1=0$.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">Deduce that $G$ is convergent.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">Find the sum to infinity of the even-numbered terms of $G$ in terms of $a$.</span></div><p style="text-align: right;">[2]</p></li></ol>

A geometric series, $G$, has common ratio $r$, $r\ne 1$, and an arithmetic series, $A$, has a non-zero first term $a$.

The first three terms of $G$ are equal to the seventh, third and first term of $A$ respectively.

Find the sum to infinity of the even-numbered terms of $G$ in terms of $a$.

APGP

H2 Math

International Baccalaureate Higher Level Mathematics

ASRJC APGP Tutorial Q2

ASRJC APGP Tutorial Q2

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