How do you find the next four terms of the arithmetic sequence 31, 24, 17, ...?

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Answer 1 · 2017-01-07T14:55:11

The reqd. next four terms are,

#T_4=10, and, T_5=3, T_6=-4, T_7=-11#.

We find that, for the given Arithmetic Sequence (A.S.),

The First Term #=a=31,# &, the Common Difference

#d=24-31=17-24=...=-7#.

Now, we know that, for such an A.S., #T_n=a+d(n-1)#

#:. T_n=31-7(n-1)=38-7n#.

Hence, the reqd. next four terms are,

#T_4=38-7(4)=10," &, similarly, "T_5=3, T_6=-4, T_7=-11#.