Find the 78 th term of the arithmetic sequence $$ 14,5,-4, \ldots $$

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The 78th term of the sequence is -679. To find the 78th term of the arithmetic sequence given by $$ 14, 5, -4, \ldots $$, we first need to identify the first term and the common difference of the sequence. The first term $$ a $$ is: $$ a = 14 $$ Next, we calculate the common difference $$ d $$ by subtracting the first term from the second term: $$ d = 5 - 14 = -9 $$ Now that we have the first term $$ a = 14 $$ and the common difference $$ d = -9 $$, we can use the formula for the $$ n $$-th term of an arithmetic sequence, which is given by: $$ a_n = a + (n-1)d $$ To find the 78th term ($$ n = 78 $$): $$ a_{78} = 14 + (78 - 1)(-9) $$ $$ = 14 + 77 \cdot (-9) $$ $$ = 14 - 693 $$ $$ = 14 - 693 = -679 $$ Thus, the 78th term of the arithmetic sequence is: $$ \boxed{-679} $$

Find the 78 th term of the arithmetic sequence \( 14,5,-4, \ldots \)

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Find the 78 th term of the arithmetic sequence \( 14,5,-4, \ldots \)

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