The 1st term of an A.p is -8.the ratio of the 7th term to the 9th term is 5:8.Find the common difference
Let the common difference be denoted by d.
Using the formula for the nth term of an arithmetic progression:
a1 = -8 (1st term)
a7 = a1 + 6d (7th term)
a9 = a1 + 8d (9th term)
We are given that the ratio of the 7th term to the 9th term is 5:8. In other words:
a7/a9 = 5/8
Substituting in the values we have:
(a1 + 6d)/(a1 + 8d) = 5/8
(-8 + 6d)/(-8 + 8d) = 5/8
Cross-multiplying and simplifying:
40 - 32d = -40 - 40d
8d = 80
d = 10
Therefore, the common difference is 10.