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

##### 1 Answer

Jun 15, 2017

#### 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#