Respuesta :
Answer: For 18 months the last term is 18 and the sum is 171. For 24 months the last term is 24 and the sum is 300. For 30 months the last term is 30 and the sum is 465.
Explanation:
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,
[tex]1+2+3+4+5+6+7+8+9+10+11+12=78[/tex]
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} [2a+(n-1)d][/tex]
Similarly, for 18 months the last term is 18 and its sum is,
[tex]S_{18}=\frac{18}{2} [2(1)+(18-1)(1)][/tex]
[tex]S_{24}=9(19)[/tex]
[tex]S_{24}=171[/tex]
Similarly, for 24 months the last term is 24 and its sum is,
[tex]S_{24}=\frac{24}{2} [2(1)+(24-1)(1)][/tex]
[tex]S_{24}=12(25)[/tex]
[tex]S_{24}=300[/tex]
Similarly, for 300 months the last term is 30 and its sum is,
[tex]S_{30}=\frac{30}{2} [2(1)+(30-1)(1)][/tex]
[tex]S_{24}=15(31)[/tex]
[tex]S_{24}=465[/tex]
Therefore, the last term for 18 month is 18 and its sum is 171. The last term for 24 month is 24 and its sum is 300. The last term for 30 month is 30 and its sum is 465.
From the arithmetic progression, the last term in a 30 months period is 30 and the sum is 465.
How to calculate arithmetic progression
From the information 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.
Therefore, when there are 30 terms, the sum will be:
= 30/2[2(1) + (30 - 1)(1)]
= 15 × 31
= 465
In conclusion, the sum of the terms is 465.
Learn more about arithmetic progression on:
https://brainly.com/question/24205483
