Question

Find the first term and the difference in an arithmetic sequence if the 100th term is 13 and the 200th term is 82. d = ______(simplify the answer using an integer or simplified fraction)

Answer 1

We will have the following:

*First: We know that arithmetic sequences follow:

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

*Second: From the information given we will have:

a100:

`13=a_1+d(100-1)\Rightarrow13=a_1+99d`

a200:

`82=a_1+d(200-1)\Rightarrow82=a_1+199d`

Then we will find the common difference:

`d=(82-13)/(200-100)\Rightarrow d=(69)/(100)\Rightarrow d=0.69`

So, the common difference is 0.69.

*Third: We determine the first term:

`13=a_1+0.69(99)\Rightarrow_{}13=a_1+68.31`
`\Rightarrow a_1=-55.31\Rightarrow a_1=-(5531)/(100)`

So, the first term is -55.31.