Question

If the nth term of two A.Ps 9,7,5,... and 24,21,18,.... are the same.find the value of n and that term

Answer 1

Answer:

below

Step-by-step explanation:

for the first given series :

a= 9

d=cd= 7-9= -2

⇒Tn= a+[n-1]d

=9=[n-1]{-2}

=9-2n+2

⇒Tn= 11-2n.

for the second series:

a=24

d=cd= 21-24= -3

⇒Tn= a+[n-1]d

=24+[n-1]{-3}

=24-3n+3

=27-3n

now, its given that the nth term of the two AP's are equal

⇒Tn=Tn

⇒11-2n = 27-3n

⇒27-11=-3n+2n

⇒16=n

or hence the value of n is 16

therefore....value of  the 16th tern = a+15d

hence of the first AP ,, we had a=9 and d= -2

⇒a+15d= 9+15{-2}

=9-30

= -21

therefore.... for the second AP

we had a=24 and d= -3

⇒a+15d= 24 + 15{-3}

=24-45

= -21

hence its clear that the nth term of the two given series of AP's are equal and the 16th term of the two AP's are also equal