For the Rule of 78, for a 12-month period, the last term in the sequence is 12 and the series sums to 78.

For an 10 month period, the last term is and the series sum is .

For a 15 month period, the last term is and the series sum is .

For a 20 month period, the last term is and the series sum is .

Step-by-step explanation:

The formula for determining the nth term of an arithmetic sequence is expressed as

Sn = n/2(a + l)

Confirming the rule of 78, the last term is 12 and the first term is 1. Therefore

78 = 12/2(1 + 12)

78 = 6(1 + 12)

78 = 6 + 72

For a 10 month period, the last term is 10, the sum of the series, S10 is

S10 = 10/2(1 + 10)

S10 = 5 × 11 = 55

For a 15 month period, the last term is 15, the sum of the series, S15 is

S15 = 15/2(1 + 15)

S15 = 7.5 × 16 = 120

For a 20 month period, the last term is 20, the sum of the series, S20 is

S20 = 20/2(1 + 20)

S20 = 10 × 21 = 210

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