Find the 31st term of an A. P. whose 10th term is 38 and 16th term is 74.
Let first term of AP is a and common difference is d.
Use formula of tn=a+(n−1)d.......(i)
Given, 10th term is 38 and 16th term is 74.
So, substitute n=10 and 16 in equation(i), we get
t10=a+(10−1)d=38 and t16=a+(16−1)d=74
⇒a+9d=38 and a+15d=74
Substitute a=38−9d in a+15d=74, we get
Substitute d=6 in a=38−9d, we get
Thus, 31th term is t31=a+30d
Substitute, a=−16 and d=6 in above expression.