Question

In an arithmetic sequence, = 5 and = 11.

Answer 1

Answer:

1134.62 (THE SUM OF 20 TERMS)

Step-by-step explanation:

First we write out our given information:

a8=2a2

a11=18

an is an arithmetic sequence.

Where here an means the nth term of our sequence.

What does an arithmetic sequence mean? It means to get to the next term in your sequence you add a constant (c) each time:

an+1=an+c

Equivalently:

an+1−an(n+1)−n=c

So an is of slope c (c2 is another constant):

an=cn+c2

Where here c2=a0 (Substitute in n=0 and see why that has to be the case if we let a0 exist)

Now we use the other given information to try to come up with a solution.

Let n=2:

a2=2c+c2

Let n=8, using the above equation we have:

a8=8c+c2=2a2=4c+2c2

Let n=11

a11=18

a11=11c+c2

But a11−a8=(11c+c2)−(8c+c2)=3c

Hence, a11=3c+a8

a11=3c+4c+2c2=18

a11=3c+8c+c2=18