For an 18 month period, the last term is and the series sum is .
For a 24 month period, the last term is and the series sum is .
For a 30 month period, the last term is and the series sum is .
To find the first term and the common difference of a given arithmetic series, we can use the formula:
S = (n / 2) * (2a + (n - 1) * d)
Where:
S = Series sum
n = Number of terms
a = First term
d = Common difference
Let's use this formula to find the first term and the common difference for each case:
1. For an 18-month period:
Given that the last term is T18 and the series sum is S18, we can write:
S18 = (18 / 2) * (2a + (18 - 1) * d)
Now we need the values of T18 and S18 to solve for a and d.
2. For a 24-month period:
Given that the last term is T24 and the series sum is S24, we can write:
S24 = (24 / 2) * (2a + (24 - 1) * d)
Now we need the values of T24 and S24 to solve for a and d.
3. For a 30-month period:
Given that the last term is T30 and the series sum is S30, we can write:
S30 = (30 / 2) * (2a + (30 - 1) * d)
Now we need the values of T30 and S30 to solve for a and d.
Please provide the values of T18, S18, T24, S24, T30, and S30 to continue solving for a and d in each case.