Mathematics 2014 JAMB Past Questions - Question 19: The 4th term of an A.P is 13 while the 10th term is 31.find the 24th term.

Correct Answer

D

Explanation

a +3d = 13 ......................(1)a+9d = 31 ..........................(2)(2) - (1): 6d = 18To find the 24th term of an arithmetic progression (A.P.), we need to determine the common difference (d) first. Given that the 4th term is 13 and the 10th term is 31, we can use these two terms to find the common difference.The formula for the nth term of an A.P. is given by:Tn = a + (n - 1)dwhere Tn is the nth term, a is the first term, n is the position of the term, and d is the common difference.Using the 4th term, we have:13 = a + (4 - 1)d13 = a + 3d ---(1)Using the 10th term, we have:31 = a + (10 - 1)d31 = a + 9d ---(2)Now, we have a system of two equations (equations 1 and 2) with two variables (a and d). We can solve this system to find the values of a and d.Subtracting equation (1) from equation (2), we get:31 - 13 = (a + 9d) - (a + 3d)18 = 6dd = 3Substituting the value of d back into equation (1), we can solve for a:13 = a + 3(3)13 = a + 9a = 4Now that we have the values of a = 4 and d = 3, we can find the 24th term using the formula:Tn = a + (n - 1)dT24 = 4 + (24 - 1)3T24 = 4 + 23 * 3T24 = 4 + 69T24 = 73Therefore, the 24th term of the arithmetic progression is 73.d = 18/6 = 3from (1), a+3 (3) = 13a+9 =13a = 13 -9= 4Hence, T24 = a +23d = 4+23x3 = 4+69 = 73