Mathematics 2011 JAMB Past Questions - Question 22: The second term of a geometric series is 4 while the fourth term is 16.Find the sum of the first five terms.

Correct Answer

B

Explanation

S a(rⁿ¯1)/r- 1S = 2(2⁵ - 1) /2-1 = 2X 31 /1 = 62 Let's denote the first term of the geometric series as 'a' and the common ratio as 'r'.Given that the second term is 4, we can write:ar = 4 ...(1)Given that the fourth term is 16, we can write:ar³ = 16 ...(2)Dividing equation (2) by equation (1), we get:(ar³)/(ar) = 16/4Simplifying, we have:r² = 4Taking the square root of both sides, we get:r = ±2Since the common ratio cannot be negative (as it is a geometric series), we take r = 2.Substituting this value of r into equation (1), we have:a(2) = 4Simplifying, we get:2a = 4a = 2Now we have the first term 'a' as 2 and the common ratio 'r' as 2.The sum of the first five terms of a geometric series can be calculated using the formula:S5 = a(1 - r⁵) / (1 - r)Substituting the values, we have:S5 = 2(1 - 2⁵) / (1 - 2)Simplifying, we get:S5 = 2(1 - 32) / (1 - 2)S5 = 2(-31) / (-1)S5 = 62Therefore, the sum of the first five terms of the geometric series is 62.