Answer:
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.
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,
![S_n=(n)/(2)[a+l]](https://img.qammunity.org/2019/formulas/mathematics/college/evwvt755gfux3comzq860ygmatnhtutefa.png)
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.
![S_(10)=(10)/(2)[1+10]](https://img.qammunity.org/2019/formulas/mathematics/college/9eu2auqbaxu6jphxlivxjkpmhcbfsft766.png)
![S_(10)=5[11]](https://img.qammunity.org/2019/formulas/mathematics/college/57nhhxx2utfdp0mtr53djgvqb3eh0vu57m.png)

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.
![S_(15)=(15)/(2)[1+15]](https://img.qammunity.org/2019/formulas/mathematics/college/o6op2wd951lciphyhd76rbws7nhn3sn6xo.png)
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.
![S_(20)=(20)/(2)[1+20]](https://img.qammunity.org/2019/formulas/mathematics/college/lqy5sjxchlubvxjq6zx9gu0cddzbqut6ek.png)
![S_(20)=10[21]](https://img.qammunity.org/2019/formulas/mathematics/college/jbuou79j9nknt09p02ixq6hg7gw03tg7de.png)
