What is the first term of an arithmetic sequence in which the seventh term is 3 and the sixteenth term is -15?

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Answer 1 · 2015-07-17T22:16:33

The first term of the sequence is #color(red)(15)#.

We know that #a_7 = 3# and #a_16 = -15#.

We also know that #a_n = a_1 + (n-1)d#.

#a_16 = a_1 + (16-1)d#

Equation (1): #-15 = a_1 + 15d#

and

#a_7 = a_1 + (7-1)d#

Equation (2): #3 = a_1 + 6d#

Subtract Equation (2) from Equation (1).

#-15-3 = 15d-6d#

#-18 = 9d#

#d = -18/9#

Equation (3): #d= -2#

Substitute Equation (3) in Equation (1).

#-15 = a_1 + 15d#

#-15 = a_1 + 15(-2) = a_1 -30#

#a_1 = 30-15#

#a_1 = 15#