Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
178
We are given that a11=38 and a16=73 where, a11 is the 11th term and a16 is the 16th term of an AP.
Using formula an=a+(n−1)d, to find nth term of arithmetic progression, we get;
38=a+(11−1)d
73=a+(16−1)d
⇒38=a+10d ....(1)
⇒73=a+15d .....(2)
These are equations consisting of two variables. Let’s solve them using substitution method.
We have,
38=a+10d
⇒ a=38−10d
Let’s put value of a in the equation (2), we get
73=38−10d+15d
⇒35=5d
Therefore Common difference is, d = 7.
Putting value of d in equation (1), we get
38=a+70
⇒a=−32
Therefore, common difference is d=7.
First term, a=−32
Using formula an=a+(n−1)d to find nth term of arithmetic progression, we get
a31=−32+(31−1)(7) = −32+210 = 178
Therefore, 31st term of AP is 178.