MATHEMATICS The first term of an arithmetic progression is -8 the ratio of the 7th term to the 9th term is 5:8 calculate the common difference of the progression
The common difference of an arithmetic progression is the same for all terms. To calculate the common difference, we need to find the difference between two consecutive terms.
The 7th term is -8 + 6 × d and the 9th term is -8 + 8 × d, where d is the common difference.
Subtracting the two equations, we get:
-8 + 6d - (-8 + 8d) = 5 - 8
2d = -3
Therefore, the common difference is d = -3/2.
(a + 6d)/(a + 8d) = 5/8
but a = -8
(-8 + 6d)/(-8 + 8d) = 5/8
-40 + 40d = -64 + 48d
24 = 8d
d = 3
check:
term(7) = -8+18 = 10
term(9) = -8 + 24 = 16
term7/term9 = 10/16 = 5/8
my answer is correct, the bot is wrong.