Mathematics 2008 JAMB Past Questions - Question 20: The fifth term of an A.P is 24 and the eleventh term is 96.find the first term .

Correct Answer

D

Explanation

in = a+(n-1)d24 = a +(5-1)d24 = a + 4d .................(i)96 = a+ (11 -1)d96 = a + 10d .............(ii)24 = a + 4d ........ (i)96 = a + 10d ...........(ii)a = 24 -4d +10d96 = 24 - 4d +10d96 = 24 +6d96 - 24 = 6d72 = 6dd = 72 / 6d = 12a = 24 - 4da = 24 - 4 x 12a = 24 - 48a = - 24To find the first term of an arithmetic progression (A.P.), we can use the formula:nth term = a + (n - 1)dwhere a is the first term, n is the position of the term, and d is the common difference.Given that the fifth term is 24 and the eleventh term is 96, we can set up two equations using the formula:24 = a + (5 - 1)d96 = a + (11 - 1)dSimplifying these equations, we have:24 = a + 4d96 = a + 10dNow, we can solve these equations simultaneously to find the values of a and d.Subtracting the first equation from the second equation, we get:96 - 24 = (a + 10d) - (a + 4d)72 = 6dd = 12Substituting the value of d back into the first equation, we can solve for a:24 = a + 4(12)24 = a + 48a = 24 - 48a = -24Therefore, the first term of the arithmetic progression is -24.