Question

Which term of an Ap -557,-553,-549 will be the first positive term
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Answer 1

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Answer 2

a (first term) = -57

d(common difference) = second term - first term

= -553-(-557)

=-553+557

= 4

Let nth term be the first positive term of the AP.

For Any term to be positive, it should be greater than 0 .

So, an>0 .

Then,

an>0= a+(n-1)d >0

= {-557 +(n-1) × 4 }>0

={-557 +4n-4} >0

={-561+4n}>0

= -561 > - 4n

=561 > 4n

= 561/4 >n

= 140.25 > n

So, n>140 .25 ,

so, n=141 .

Therefore 1st positive term will be 141th term.

$\huge{ \bf{hope \: it \: helps :) }}$