Question

which term of the AP 53,48,43,... is its first negative term? find that term.

Answer 1

Hey Mate

your answer is here

Common difference of AP = 48-53 = -5

general term An

An = 53+(n+1)(-5)

An = 53-5(n-1)

for An negative,

53-5(n-1) < 0
n-1 > 53/5

n > 1+53/5
n > 11.6

so,

First negative term is 12 term

and it's value = 53-5(12-1) = 53-55 = -2

Answer 2

Let the first term be a.

common difference be d.

Let the first negative term be n.

nth term=a+(n-1)d

a=53

d=48-53

=-5

Now

a+(n-1)d<0

=53+(-5)(n-1)<0

=53-5n+5<0

58-5n<0

58<5n

5n>58

So the least possible value of n is 12

for which 5*12=60>58

So n must be 12.

12 th term is the first negative term.

Its value is a+(n-1)d

=53+(12-1)*(-5)

=53+(-55)

=-2

Hope it helps.