Question

Write a rule for the nth term of the sequence:
a_6 = -8, a_15 = -62 arithmetic

Answer 1

`a_n=28-6n`

Explanation:

Formula for arithmetic sequence:
`a_n=a+(n-1)d`

Given:

• 
  `a_6=-8`
• 
  `a_(15)=-62`

`a_6=a+5d=-8`

`a_(15)=a+14d=-62`

`a_(15)-a_6\implies 9d=-54`

`\implies d=-6`

Substituting found value for d into one of the equations and solving for a:

`a_6=a+(5 * -6)=-8`

`\implies a=22`

`\implies a_n=22-6(n-1)`

`\implies a_n=28-6n`