Determine the common difference and the first term of an A.P. a3=7, a7=8 Determine the common difference and the first term of an A.P. a3=7, a7=8

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We know that:

a3= a1+ 2*r = 7........(1)

a7 = a1+ 6r = 8.........(2)

Now all we have to do is solve the system in order to obtain r and a1 values:

By using thre elimination methos, we will subtract (1) from (2):

=> 4*r = 1

==> r= 1/4

...

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We know that:

a3= a1+ 2*r = 7........(1)

a7 = a1+ 6r = 8.........(2)

Now all we have to do is solve the system in order to obtain r and a1 values:

By using thre elimination methos, we will subtract (1) from (2):

=> 4*r = 1

==> r= 1/4

Now to calculate a1, we will substitute with r=1/4 in either equations:

==> a1+ 3r = 7

==> a1= 7-3r = 7- 3*1/4 = 7-3/4 = 6 1/4 = 25/6

==> a1= 25/6

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