Question

How do you write the first five terms of the arithmetic sequence given `a_3=19, a_15=-1.7`?

Answer 1

`22.45,20.725,19,17.255,15.55`

Explanation:

`"for a standard arithmetic sequence"`

`"the nth term " =a+(n-1)d`

`"where a is the first term and d the common difference"`

`"we require to find both a and d"`

`a_3=a+2d=19to(1)`

`a_(15)=a+14d=-1.7to(2)`

`"subtract "(1)" from " (2)`

`rArr12d=-20.7rArrd=-1.725`

`"substitute this value in " (1)`

`a-3.45=19rArra=22.45`

`rArra_1=22.45`

`a_2=22.45-1.725=20.725`

`a_3=20.725-1.725=19`

`a_4=19-1.725=17.255`

`a_5=17.255-1.725-15.55`