Arithmetic sequences et sn} be an arithmetic sequence that starts with an initial index of 0. the initial term is 3 and the common difference is -2. what is sz? (b) consider the arithmetic sequence: 7, 4, 1, what is the next term in the sequence?

(a) The value of is (z+1)(3-z).

(b) The next term in the sequence is -2.

Step-by-step explanation:

(a)

It is given that arithmetic sequence that starts with an initial index of 0.

The initial term is 3 and the common difference is -2.

We need to find the value of .

where, a is initial term and d is common difference.

The sum of an arithmetic sequence with  initial index 0 is

where, a is initial term and d is common difference.

Substitute n=z, a=3 and d=-2 in the above formula.

Therefore the value of is (z+1)(3-z).

(b)

The given arithmetic sequence is

7, 4, 1, ...

We need to find the term in the sequence.

In the given arithmetic sequence the first term is

The common difference of the sequence is

The first term is 7 and common difference is -3.

Add common difference in last given term, i.e., 1, to find the next term of the sequence.

Therefore the next term in the sequence is -2.

7 weeks

step-by-step explanation:

convert each fraction to the least common multiple of 20, so 3/4 = 15/20 & 1/10 = 2/20, then divide 15 by 2 and you get a little over 7, so the food will last 7 weeks.