MATHEMATICS PLEASE HELP ME!!! In an arithmetic series the 3rd term is twice the 8th term find the first 25 terms
BEEN THERE , DONE THAT
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To solve this problem, we first need to determine the values of the first term (a), the common difference (d), and then use these values to find the first 25 terms.
We know that in an arithmetic series, each term can be represented by the formula: an = a + (n - 1)d
Where:
- an is the nth term in the series
- a is the first term
- n is the position of the term in the series (1st, 2nd, 3rd, etc.)
- d is the common difference
Given that the 3rd term is twice the 8th term, we can set up the following equation:
a + 2d = a + 7d
Simplifying this equation, we get:
d = a
Therefore, the common difference (d) is equal to the first term (a).
Now, to find the first term (a), we can substitute this value into the equation and use the given information:
a + 2a = a + 7a
3a = 8a
a = 0
Now that we know the value of the first term (a = 0), we can use the formula an = a + (n - 1)d to find the first 25 terms.
Substituting the values of a and d into the formula, we get:
an = 0 + (n - 1) * 0
an = 0
Hence, the first 25 terms of this arithmetic series are all equal to 0.