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In an arithmetic sequence the $2^{\text {nd }}$ term is 9 and the $5^{\text {th }}$ term is 21. Determine

a) The first three terms of the sequence.
b) The $60^{\text {th }}$ term
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\begin{aligned}
&T_{2}=a+d=9 \quad \text { (1) } 2^{\text {nd }} \text { term }\\
&T_{5}=a+4 d=21 \quad \text { (2) } 5^{\text {th }} \text { term }\\
&3 d=12 \quad \text { (2) }-(1)\\
&\boldsymbol{d}=\mathbf{4}\\
&\therefore T_{2}=a+d=9\\
&a+4=9\\
&\boldsymbol{a}=\mathbf{5}\\
&\text { First three terms are 5; 9; 13; }\\
&T_{60}=a+59 d=5+59(4)=241\\
&\text { Hence the } 60^{\text {th }} \text { term is } 241
\end{aligned}
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