Question

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

Answer 1

Answer:

We can solve this question using the formula below-

The formula for sum of n terms is,

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

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

Here a = 1 and d = 1

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

$S_{14}=7(15)=105$

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

Here a = 1 and d = 1

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

$S_{16}=8(17)=136$

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;

$1+2+3+4+5+6+7+8+9+10+11+12+13+14= 105$

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

$1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16= 136$

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

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