Question

# Find the 31st term of an A. P. whose 10th term is 38 and 16th term is 74.

Solution

## 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=74Substitute a=38−9d in a+15d=74, we get ⇒38−9d+15d=74⇒38+6d=74⇒6d=74−38⇒d=366∴d=6Substitute d=6 in a=38−9d, we get ⇒a=38−9(6) ⇒a=38−54⇒a=−16Thus, 31th term is t31=a+30dSubstitute, a=−16 and d=6 in above expression.t31=−16+30(6)=−16+180∴t31=164MathematicsConcise MathematicsStandard X

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