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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 14 month period, the last term is and the series sum is .

For a 16 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.

Respuesta :

Answer:

We can solve this question using the formula below-

The formula for sum of n terms is,

[tex]S_n=\frac{n}{2} [2a+(n-1)d][/tex]

For 14 months the last term is 14 and its sum is,

Here a = 1 and d = 1

[tex]S_{14}=\frac{14}{2} [2(1)+(14-1)(1)][/tex]

[tex]S_{14}=7(15)=105[/tex]

For 16 months the last term is 16 and its sum is,

Here a = 1 and d = 1

[tex]S_{16}=\frac{16}{2} [2(1)+(16-1)(1)][/tex]

[tex]S_{16}=8(17)=136[/tex]

OR

We can also solve this using simple addition like-

1. For a 14 month period the last term in the sequence is 14 and the series sum is;

[tex]1+2+3+4+5+6+7+8+9+10+11+12+13+14= 105[/tex]

2. For a 16 month period, the last term is 16 and the series sum is;

[tex]1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16= 136[/tex]

3. For a 16 month period, the last term is 20 and the series sum is;

[tex]1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20=210[/tex]

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