Question

what least no of the term of the sequence 17,79/5,73/5 should be taken so that the sum is negative

Answer 1

Hey

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Answer 2

Answer:

The minimum number of terms is 30 which make the sum negative.

Step-by-step explanation:

Given : Sequence $17,\frac{79}{5},\frac{73}{5}$

To find : What least no of the term of the sequence should be taken so that the sum is negative?

Solution :  

Sequence $17,\frac{79}{5},\frac{73}{5}$

The first term of the sequence is a=17

The common difference of the sequence is  

$d=\frac{79}{5}-17=\frac{79-85}{5}=-\frac{6}{5}$

The sum of the arithmetic sequence is  

$S_n=\frac{n}{2}(a+(n-1)d)$

We have given,  Sum is negative i.e, $S_n<0$

So, $\frac{n}{2}(2(17)+(n-1)\frac{-6}{5})<0$

$\frac{n}{2}(17+\frac{85}{5}+\frac{6}{5}-\frac{6}{5})<0$

$17+\frac{91-6n}{5}<0$

$\frac{91-6n}{5}<-17$

$91-6n<-85$

$176<6n$

$n>\frac{176}{6}$

$n>29$

Therefore, The minimum number of terms is 30 which make the sum negative.