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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