Respuesta :
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.
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,
[tex]S_n=\frac{n}{2}[a+l][/tex]
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.
[tex]S_{10}=\frac{10}{2}[1+10][/tex]
[tex]S_{10}=5[11][/tex]
[tex]S_{10}=55[/tex]
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.
[tex]S_{15}=\frac{15}{2}[1+15][/tex]
[tex]S_{15}=7.5[16][/tex]
[tex]S_{15}=120[/tex]
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.
[tex]S_{20}=\frac{20}{2}[1+20][/tex]
[tex]S_{20}=10[21][/tex]
[tex]S_{20}=210[/tex]
