Question

Find the first term, a1, of an arithmetic sequence if a15 = 136 and a19 = 168.

32/23

8

24

23

Answer 1

Since
`a_n` is an arithmetic sequence, there is some constant
`d` by which consecutive terms differ. This means


`a_(16)=a_(15)+d`

`a_(17)=a_(16)+d=a_(15)+2d`

`a_(18)=a_(17)+d=a_(15)+3d`

`a_(19)=a_(18)+d=a_(15)+4d`


`168=136+4d\implies d=8`

By a similar token, we can express
`a_(15)` in terms of
`a_1`:


`a_2=a_1+d`

`a_3=a_2+d=a_1+2d`

`\cdots`

`a_(15)=a_(14)+d=a_1+14d`


`136=a_1+14\cdot8\implies a_1=24`