Mathematics 2019 JAMB Past Questions - Question 25: The 4th term of an AP is 13 while the 10th term is 31. Find the 21st term.

Correct Answer

C

Explanation

To find the 21st term of an arithmetic progression (AP) when the 4th term is 13 and the 10th term is 31, we can use the formula for the nth term of an AP:\[ a_n = a_1 + (n-1)d \]Where:- \( a_n \) is the nth term- \( a_1 \) is the first term- \( n \) is the term number- \( d \) is the common differenceWe are given that the 4th term is 13 and the 10th term is 31. Using these, we can form two equations:\[ a_4 = a_1 + 3d = 13 \]\[ a_{10} = a_1 + 9d = 31 \]Subtracting the first equation from the second gives:\[ 6d = 18 \]\[ d = 3 \]Now that we have the common difference, we can find the first term by substituting \( d = 3 \) into the first equation:\[ a_1 + 3(3) = 13 \]\[ a_1 + 9 = 13 \]\[ a_1 = 4 \]Finally, we can find the 21st term using the formula:\[ a_{21} = 4 + 20(3) = 64 \]So, the 21st term of the AP is 64. Therefore, the answer is C. 64.