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Question Number 21276 by ketto last updated on 18/Sep/17

	Answered by $@ty@m last updated on 19/Sep/17

	$(a) G i v e n$ $t_{3} = 18 \Rightarrow {a r}^{2} = 18 - - (1)$ $t_{5} = 162 \Rightarrow {a r}^{4} = 162 - - (2)$ $D i v i d i n g (2) b y (1)$ $r^{2} = 9 \Rightarrow r = \pm 3$ $∴ f r o m (1)$ $a = 2$ $(b) G i v e n$ $t_{8} = t_{5} + 9 \Rightarrow a + 7 d = a + 4 d + 9 \Rightarrow d = 3$ $a n d t_{10} = 10 t_{2} \Rightarrow a + 9 d = 10 (a + d)$ $\Rightarrow a + 9 d = 10 a + 10 d$ $\Rightarrow - 9 a = d$ $\Rightarrow - 9 a = 3$ $\Rightarrow a = \frac{- 1}{3}$
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