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

1) For an 10 month period, the last term is 10 and the series sum is 55.

2) For a 15 month period, the last term is  15 and the series sum is 120.

3) For a 20 month period, the last term is 20 and the series sum is 210.

Step-by-step explanation:

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

To find :

1) For an 10 month period, the last term is__ and the series sum is__ .

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

3) For a 20 month period, the last term is__ and the series sum is__ .

Solution :

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

1+2+3+4+5+6+7+8+9+10+11+12=78

It is an AP with first term 1 and common difference 1.

The formula for sum of n terms is,

Where, a is the first term and l is the last term

1) For an 10 month period, the last term is__ and the series sum is__ .

For an 10 month period, the last term is 10.

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

For an 15 month period, the last term is 15.

3) For a 20 month period, the last term is__ and the series sum is__ .

For an 20 month period, the last term is 20.

Can u answer my question

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

For a 10 month period the last term is 10 and the series sum is 55. For a 15 month period the last term is 15 and the sum is 120. For a 20 month period the last term is 20.
If u want the sum then it is 210.

Hope this helps you!