Suppose the 4th term of an arithmetic sequence is 27, and the 8th term is 59.
1. What are the first term and the common difference?
2. Write a function for the sequence.

The first term is 3 and common difference is 8.

And

The formula for sequence is:

Function is:

Step-by-step explanation:

Given that

The general formula for arithmetic sequence is:

Here

a is the first term

n is the term number

and d is the common difference

for 4th term

For 8th term

subtracting equation 1 from equation 2

Putting d = 8 in equation 1

Now for the function

The sequence can also be expressed as a function as:

Hence,

The first term is 3 and common difference is 8.

And

The formula for sequence is:

Function is:

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

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