Question

which is the larger, the 10th term of an arithmetic sequence that begins with the terms 5 and 10? show work that justify your answer

Answer 1

Arithmetic Sequence

To answer this question, we need to find the value of the 10th term of the arithmetic sequence. An arithmetic sequence is given by:

`a_n=a_1+(n-1)d`

In this case, we have that:

a1 = 0

n = 10

d = 100 - 0 ---> d = 100

Then, applying the previous formula, we have:

`a_(10)=0+(10-1)\cdot100\Rightarrow a_(10)=9\cdot100\Rightarrow a_(10)=900`

Then, the 10th term in this arithmetic sequence is equal to 900.

Geometric Sequence

We need to apply the formula to find a term in a geometric sequence:

`a_n=a_1\cdot r^(n-1)`

We have that the first two terms are 5 and 10. The common ratio, r, is given by dividing the second term by the first term:

`r=(10)/(5)\Rightarrow r=2`

Then, we have:

a1 = 5

r = 2

n = 10

Therefore:

`a_(10)=5\cdot2^(10-1)\Rightarrow a_(10)=5\cdot2^9\Rightarrow a_(10)=5\cdot512\Rightarrow a_(10)=2560`

The 10th term in this geometric sequence is equal to 2560.

Hence, the 10th term of the geometric sequence here is greater than the one in the arithmetic sequence, that is:

• 10th term geometric sequence = 2560

,

• 10th term arithmetic sequence = 900