`a_3 = 19, a_15 = -1.7` Write the first 5 terms of the arithmetic sequence.

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`a_3=19`

`a_15=-1.7`

Let `a_1`  be the first term and d be the common difference of the sequence.

`a_15=a_1+14d`

`a_1+14d=-1.7`   ---------- (1)

`a_3=a_1+2d`

`a_1+2d=19`         ----------- (2)

Now let's solve the equations 1 and 2 to get the `a_1` and d,

Subtract equation 2 from equation 1,

`14d-2d=-1.7-19`

`12d=-20.7`

`d=-20.7/12`

`d=-1.725`

Plug the value of d in equation 2,

`a_1+2(-1.725)=19`

`a_1-3.45=19`

`a_1=19+3.45`

`a_1=22.45` 

`a_2=a_1+d`

`a_2=22.45+(-1.725)`

`a_2=20.725` 

`a_3=a_2+d`

`a_3=20.725+(-1.725)` 

`a_3=19`

`a_4=a_3+d`

`a_4=19+(-1.725)`

`a_4=17.275`

`a_5=a_4+d`

`a_5=17.275+(-1.725)`

`a_5=15.55`

So the first five terms of the sequence are 22.45,20.725,19,17.275 and 15.55

Approved by eNotes Editorial Team