Question
Explain the first term of an Arithmetic progression (A. P) is -8.the ratio of the 7th term to the 9th term is 5:8. Calculate the common difference of the progression
Answers
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The common difference of an arithmetic progression (A.P) is the difference between any two consecutive terms. In this case, the first term is -8 and the common difference can be calculated by subtracting the first term from the second term.
Therefore, the common difference of the progression is -8 - (-3) = -5.
To calculate the 7th term and the 9th term, we can use the formula for the nth term of an A.P.
The nth term of an A.P. = a + (n - 1)d
Where a is the first term, n is the number of the term and d is the common difference.
Therefore, the 7th term = -8 + (7 - 1) (-5) = -8 - 30 = -38
The 9th term = -8 + (9 - 1) (-5) = -8 - 40 = -48
The ratio of the 7th term to the 9th term is -38 : -48 = 5 : 8.
Therefore, the common difference of the progression is -8 - (-3) = -5.
To calculate the 7th term and the 9th term, we can use the formula for the nth term of an A.P.
The nth term of an A.P. = a + (n - 1)d
Where a is the first term, n is the number of the term and d is the common difference.
Therefore, the 7th term = -8 + (7 - 1) (-5) = -8 - 30 = -38
The 9th term = -8 + (9 - 1) (-5) = -8 - 40 = -48
The ratio of the 7th term to the 9th term is -38 : -48 = 5 : 8.