The fourth term in an arithmetic sequence is 18 and the seventh term is 42. if the first term is a1, which is an equation for the nth term of this sequence? 1. an = 8n + 10 2. an = 8n − 14 3. an = 16n + 10 4. an = 16n − 38

Option 2nd is correct

Step-by-step explanation:

The nth term for the arithmetic equation is give by:

            ....[A]

where,

is the first term

d is the common difference and

n is the number of term.

As per the statement:

The fourth term in an arithmetic sequence is 18 and the seventh term is 42

⇒ and

then by above definition we have;

            .....[1]

           .....[2]

Subtract equation [1] from [2] we have;

3d = 24

Divide both sides by 3 we have;

d = 8

Substitute in [1] we have;

Subtract 24 from both sides we have;

We have to find the equation for the nth term of this sequence

Substitute the given values in [A] we have;

⇒

⇒

Therefore, an equation for the nth term of this sequence is,

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.