If the third term of a geometric sequence is 36 and the eighth term is 8748, how do you find the first term?

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Answer 1 · 2015-11-08T08:53:25

$A_1 = 4$

$A_n = A_1r^(n - 1)$

$=> A_3 = A_1r^2$

$=> 36 = A_1r^2$

$A_8 = A_1r^7$

$=> 8748 = A_1r^7$

If we divide the second equation by the second

$8748/36 = (A_1r^7)/(A_1r^2)$

$=> 243 = r^5$

$=> r = 3$

Let's use the first equation to find $A_1$

$A_3 = A_1r^2$

$=> 36 = A_1*3^2$

$=> 36 = 9A_1$

$=> A_1 = 4$