In the arithmetic sequence t_1, t_2, t_3, , t_n, , t_1=23 and...

Question

In the arithmetic sequence t_1, t_2, t_3, , t_n, , t_1=23 and t_n=t_n-1-3 for each n>1. What is the value of n when t_n=-4 ?

GMAT Panda · Accepted Answer

10 We translate the given first term t_1 = 23 We apply the formula for an evenly spaced (arithmetic) sequence t_n = t_1 + (n-1)d d = -3 We substitute t_n=-4, t_1=23, and d=-3 into the formula -4 = 23 + (n-1)(-3) We isolate n-1 by subtracting 23 from both sides -4 - 23 = -3(n-1) -27 = -3(n-1) We solve for n by dividing by -3 and then adding 1 -27/-3 = n-1 9 = n-1 n = 10

Explanation	Calculations	Help
$We translate the given first term$	$t_{1} = 23$
$We apply the formula for an evenly spaced (arithmetic) sequence$	$t_{n} = t_{1} + (n - 1) d d = - 3$
$We substitute t_{n} = - 4, t_{1} = 23, and d = - 3 into the formula$	$- 4 = 23 + (n - 1) (- 3)$
$We isolate n - 1 by subtracting 23 from both sides$	$- 4 - 23 = - 3 (n - 1) - 27 = - 3 (n - 1)$
$We solve for n by dividing by - 3 and then adding 1$	$\frac{- 27}{- 3} = n - 1 9 = n - 1 n = 10$

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