Question

Find the first term of the arithmetic sequence in which a32=389/4 and the common difference is 3/4

Answer 1

74

Explanation:

Given

`a_(32)=(389)/(4)\\ \\d=(3)/(4)`

Use the formula for the
`n^(th)` term of arithmetic sequence:

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

For the
`a_(32),` you have that
`n=32,` so

`a_(32)=a_1+(32-1)d\\ \\(389)/(4)=a_1+31\cdot (3)/(4)\\ \\(389)/(4)=a_1+(93)/(4)\\ \\a_1=(389)/(4)-(93)/(4)\\ \\a_1=(296)/(4)\\ \\a_1=74`