In the arithmetic sequence $t_{1}, t_{2}, t_{3}, \ldots, t_{n}, \ldots, t_{1}=23$ and $t_{n}=t_{n-1}-3$ for each $n>1$. What is the value of $n$ when $t_{n}=-4$ ?

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In the arithmetic sequence t_{1}, t_{2}, t_{3}, \dots, t_{n}, \dots, t_{1} = 23 and t_{n} = t_{n - 1} - 3 for each n > 1 . What is the value of n when t_{n} = - 4 ?

Explanation	Calculations	Help
$We translate the given first term$	$t_{1} = 23$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We apply the formula for an evenly spaced (arithmetic) sequence$	$t_{n} = t_{1} + (n - 1) d d = - 3$	Theory & Tactics Method Card SEQ1 Click to view full details
$We substitute t_{n} = - 4, t_{1} = 23, and d = - 3 into the formula$	$- 4 = 23 + (n - 1) (- 3)$
$We isolate n - 1 by subtracting 23 from both sides$	$- 4 - 23 = - 3 (n - 1) - 27 = - 3 (n - 1)$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We solve for n by dividing by - 3 and then adding 1$	$\frac{- 27}{- 3} = n - 1 9 = n - 1 n = 10$	Theory & Tactics Method Card EQUA1-B Click to view full details

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In the arithmetic sequence t_{1}, t_{2}, t_{3}, \dots, t_{n}, \dots, t_{1} = 23 and t_{n} = t_{n - 1} - 3 for each n > 1 . What is the value of n when t_{n} = - 4 ?

Explanation	Calculations	Help
$We translate the given first term$	$t_{1} = 23$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We apply the formula for an evenly spaced (arithmetic) sequence$	$t_{n} = t_{1} + (n - 1) d d = - 3$	Theory & Tactics Method Card SEQ1 Click to view full details
$We substitute t_{n} = - 4, t_{1} = 23, and d = - 3 into the formula$	$- 4 = 23 + (n - 1) (- 3)$
$We isolate n - 1 by subtracting 23 from both sides$	$- 4 - 23 = - 3 (n - 1) - 27 = - 3 (n - 1)$	Theory & Tactics Method Card EQUA1-A Click to view full details
$We solve for n by dividing by - 3 and then adding 1$	$\frac{- 27}{- 3} = n - 1 9 = n - 1 n = 10$	Theory & Tactics Method Card EQUA1-B Click to view full details

Scroll horizontally to view all columns

10