The 2nd term of an arithmetic progression is (1/2) and the sum of the first 14th terms is -70. Find (a) the common difference
(b) the last term.​

The common difference is -1.

The last term (the 14th term) is -11.5.

Step-by-step explanation:

In an arithmetic sequence, the second term is 0.5 and the sum of the first 14 terms is -70.

We want to determine the: (a) common difference and (b) the last term.

We can write an explicit formula to represent the sequence. An arithmetic sequence can be modeled by the formula:

Where a is the initial term, d is the common difference, and n represents the nth term.

Since the second term is 0.5:

Simplify:

The sum of an arithmetic sequence is given by the formula:

Where k is the number of terms and x_k is the last term.

Since the sum of the first 14 terms is -70, S = -70 and k = 14:

Using our explicit formula, the last term is:

Substitute:

Simplifiy:

Rewrite the equation for the second term:

Substitute:

Simplify:

Solve for d:

Hence, our common difference is -1.

Solve for a, the initial term:

So, our explicit formula is now:

So, the last term (which is 14) is:

the answer is d on edge

step-by-step explanation:

answer:

step-by-step explanation:

here, the total dishes = 10

dishes having meat = 3 ( chicken, meatloaf and hamburger )

thus, the probability of having meat on the chosen dishes = number of dishes having meat / total dishes

=

therefore, the probability of not having meat = 1- the probability of having meat on the chosen dishes

=

=

=

⇒ option b is correct.