An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference.
sum(8) = 4(2a + 7d)
= 8a + 28d = 24 + 28d
sum(5) = (5/2)(2a + 4d)
= 5a + 10d
= 15 + 10d
24+28d = 2(15+10d)
solve for d, let me know what you get
3/4
2[(5 * 3) + 10d] = (8 * 3) + 28d
I am not understand yet....🤔
To find the common difference, we can use the formula for the sum of an arithmetic progression. The sum of the first n terms of an arithmetic progression is given by the formula Sn = n/2 * (2a + (n-1)d), where a is the first term and d is the common difference.
Given that the first term is 3, we can write the sum of the first 8 terms as S8 = 8/2 * (2*3 + (8-1)d) = 4(6 + 7d) = 24 + 28d.
Similarly, the sum of the first 5 terms is S5 = 5/2 * (2*3 + (5-1)d) = 2(6 + 4d) = 12 + 8d.
According to the problem, the sum of the first 8 terms (S8) is twice the sum of the first 5 terms (2*S5):
24 + 28d = 2(12 + 8d)
Let's solve this equation for d:
24 + 28d = 24 + 16d
12d = 0
d = 0
Therefore, the common difference in this arithmetic progression is 0.