(a)

The amount of weight that a horse gains is of the previous months weight gain, .

The horse gained  pounds in the first month, .

The explicit formula is .

Substitute and .

The explicit formula for the horse gain is .

Find the sigma notation of the horses weight gain for the first five months.

The sigma notation of geometric series , where is upper bound.

The upper bound is .

Therefore, the sigma notation of th ehorse weight gain is .

(b)

Find the weight of the horse gain in the fourth month.

The explict formula of the horse weight is .

Substitute .

Therefore, the horse gained pounds in the fourth month.

(c)

Find the sum of the series after five months when the birth weight of the horse is pounds.

The sum of the series is .

Substitute and and .

.

The weight of the horse after five months is pounds.

(d)

The horse cannot continue to grow at this rate indefinitely because its body will eventually stop growing.

(a) The sigma notation of th ehorse weight gain is .

(b)  The horse gained pounds in the fourth month.

(c) The weight of the horse after five months is pounds.

(d) The horse cannot continue to grow at this rate indefinitely because its body will eventually stop growing.