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emmasim [6.3K]
3 years ago
8

What is the 100th term if the sequence? 5 ,1 ,-3,-7

Mathematics
1 answer:
wel3 years ago
3 0
<span>5 ,1 ,-3,-7  ?  what the dickens is going on?

notice, from 5 to 1, is really -4 units,

from 1 to -3, is -4 units as well, 1 -4 = -3  and so on.

so, to get the next term's value, you simply subtract 4 from the current one, namely -4 is the "common difference".

and we also know the first term is 5, ok... then

</span>\bf n^{th}\textit{ term of an arithmetic sequence}\\\\&#10;a_n=a_1+(n-1)d\qquad &#10;\begin{cases}&#10;n=n^{th}\ term\\&#10;a_1=\textit{first term's value}\\&#10;d=\textit{common difference}\\&#10;----------\\&#10;d=-4\\&#10;a_1=5\\&#10;n=100&#10;\end{cases}&#10;\\\\\\&#10;a_{100}=5+(100-1)(-4)\implies a_{100}=5+(99)(-4)&#10;\\\\\\&#10;a_{100}=5-396\implies a_{100}=-391<span>
</span>
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