Question

How do you find the first term and common difference if The 6th term of the sequence is -2, The 14th term of the sequence is -18?

Answer 1

First term: `8`
Common difference: `(-2)`

Explanation:

For an arithmetic sequence, `a_i`, with a common difference of `d`
`color(white)("XXX")color(red)(a_(k+n)=a_k+n*d)`

We are told
`color(white)("XXX")a_14=-18color(white)("XX")andcolor(white)("XX")a_6=-2`

Using `k=6` we have `n=8`
`color(white)("XXX")a_14=color(red)(a_(6+8)=a_6+8*d)`

`color(white)("XXX")-18=-2+8d`

`color(white)("XXX")rarr d=-2`

Now setting `k=1`
`color(white)("XXX")a_6=color(red)(a_(1+5)=a_1+5xx(-2))`

`color(white)("XXX")rarr -2 = a_1+(-10)`

`color(white)("XXX")rarr a_1=8`