Question

The 17th term of an Arithmetic sequence is 51. If the commons difference is 7, what is the first term ?

Answer 1

The first term is:

• 
  `a_1=-61`

Explanation:

The arithmetic sequence is defined by

`a_n=a_1+\left(n-1\right)d`

where

`a_1` is the first term

`d` is the common difference

as

the 17th term of an arithmetic sequence is 51.

i.e.
`a_(17)=51`

so

`a_n=a_1+\left(n-1\right)d`

`a_(17)=a_1+\left(17-1\right)d`

`51=a_1+\left(17-1\right)7` ∵
`n = 17`,
`a_(17)=51` ,
`d=7`

`a_1+112=51` ∵
`\left(17-1\right)\cdot \:\:7=112`

`a_1=-61`

Therefore, the first term is:

• 
  `a_1=-61`