Question

the fifth term of an arithmetic progression is 11 and its ninth term is 7. find its 16th term​

Answer 1

Answer:

16th term is 0

Step-by-step explanation:

Hope it helps ☺☺

Answer 2

Answer:

Here, The 16th term of the given A. P. is (-15).

Step-by-step explanation:

Here, As per our given question,

Let the first term of the given A. P. be a

Let the Common difference of the A. P. be d

=Fifth term of the A. P.=T5 =11

=T5=a+(n-1)×d (Where n=5)

=11=a+(5-1)×d

=11=a+4d

=a+4d=11 -(1st)eq.

Now, Ninth term of theA. P.=T9 =7

=T9=a+(n-1)×d

=7=a+(9-1)×d

=7=a+8d

=a+8d=7 -(2nd)eq.

Now, On solving both equations by elimination method, we will subtract eq. 2 from eq. 1,

= a+4d= 11

=-a-8d=-07

After solving, we get,

=4d-8d=11-7

=(-4)d=4

=d=4/(-4)

=d=(-1)

So, by putting value of x in eq. 1,we get,

=a+4×(-1)=11

=a-4=11

=a=11+4

=a=15

So, Now The 16th term of the A. P.=T16

=T16=a+(n-1)×d

=T16=15+(16-1)×(-2)

=T16=23+15×(-2)

=T16=15-30

=T16=(-15)

So, The 16th term of the given A. P. =(-15).

Thank you.