Mathematics 2010 JAMB Past Questions - Question 22: The 3rd term of an arithmetic progression is -9 and the 7th term is -29 .find the 10th term of the progression .

Correct Answer

C

Explanation

3rd term : a+2d = -9 ................. (1)7th term : a+6d = -29 ................. (2)(2) - (1) : 4d = -20therefore d = -20/4 = -5from (1) : a+2(-5) = -9 a- 10 = -9therefore a = -9+10 = 1therefore 10th term of A.P. is a +9d = 1+9(-5)= 1-45 = -To find the 10th term of an arithmetic progression, we need to determine the common difference (d) first. Given that the 3rd term is -9 and the 7th term is -29, we can use these values to find the common difference.The formula for the nth term of an arithmetic progression is given by:an = a1 + (n - 1) * dwhere:an is the nth term,a1 is the first term, andd is the common difference.Using the given information, we can set up two equations:a3 = a1 + (3 - 1) * d = -9a7 = a1 + (7 - 1) * d = -29Simplifying these equations, we get:a1 + 2d = -9 ---(1)a1 + 6d = -29 ---(2)Subtracting equation (1) from equation (2), we can eliminate a1:4d = -20Dividing both sides by 4, we find:d = -5Now that we know the common difference (d = -5), we can find the first term (a1) using equation (1):a1 + 2(-5) = -9a1 - 10 = -9a1 = -9 + 10a1 = 1Finally, we can find the 10th term (a10) using the formula for the nth term:a10 = a1 + (10 - 1) * da10 = 1 + 9 * (-5)a10 = 1 - 45a10 = -44Therefore, the 10th term of the arithmetic progression is -44.