Question

Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

please send a pic of solution if possible​

Answer 1

Answer:

Here, The 31st term of the given A. P. =178.

Step-by-step explanation:

Here, As per our given question,

=11th term of the given A. P. = T11=38

=First term=a, Common difference=d

=T11=a+(n-1)×d (Where n=11)

=38=a+(11-1)×d

=38=a+10d

=a+10d=38 -(1st)eq.

Now, 16th term of the A.P. = T16=73

=T16=a+(n-1)×d (Where n=16)

=73=a+(16-1)×d

=73=a+15d

=a+15d=73 -(2nd)eq.

Now, by solving both equations by elimination method, we would subtract 2nd eq. from the 1st,

=a+10d=38

=-a-15d=-73

After solving, we get,

=10d-15d=38-73

=(-5d)=(-35)

=5d=35 (As both sides are equal and have same sign of -)

=d=35/5

=d=7

Now, by putting the value of d in eq. 1,we get,

=a+10×(7)=38

=a+70=38

=a=38-70

=a=(-32)

Now, As per asked in question,

=31st term of the A. P. =a+(n-1)×d

=T31=(-32)+(31-1)×7

=T31=(-32)+30×7

=T31=(-32)+210

=T31=178

So, The 31st term of the given A. P. is 178.

Thank you.