the first, third and sixth terms of a linear sequence are the first three terms of an exponential sequence. find the common ratio


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Question Number 192991 by otchereabdullai@gmail.com last updated on 01/Jun/23

$t h e f i r s t, t h i r d a n d s i x t h t e r m s o f a$ $l i n e a r s e q u e n c e a r e t h e f i r s t t h r e e$ $t e r m s o f a n e x p o n e n t i a l s e q u e n c e .$ $f i n d t h e c o m m o n r a t i o$
	Answered by MM42 last updated on 01/Jun/23

	$l . s : t_{1}, t_{3}, t_{6}; t_{n} = t_{1} + (n - 1) d$ $e . s : a_{1}, a_{2}, a_{3}; a_{n} = a_{1} q^{n - 1}$ $a_{1} = t_{1} & a_{2} = t_{3} = t_{1} + 2 d & a_{3} = t_{6} = t_{1} + 5 d$ $a_{1} \times a_{3} = {(a_{2})}^{2} \Rightarrow t_{1} = 4 d$ $\Rightarrow a_{1} = 4 d & a_{2} = 6 d & a_{3} = 9 d$ $\Rightarrow q = \frac{3}{2} ✓$
	Commented by otchereabdullai@gmail.com last updated on 01/Jun/23

	$t h a n k s$
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