SOLUTION: in an arithmetic sequence, a3=-8 and a17=48 find the 20th term for the sequence

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Question 399540: in an arithmetic sequence, a3=-8 and a17=48
find the 20th term for the sequence
Found 2 solutions by ewatrrr, rahulsoni001002:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad

a%5B3%5D=a%5B1%5D%2B%282%29%2Ad+=+8  a%5B1%5D+=+8-2d

a%5B17%5D=a%5B1%5D%2B%2816%29%2Ad+=+48

    (8-2d) + 16d = 48

         14d = 40

           d = 40/14 = 20/7  and a%5B1%5D+=+8-40%2F7+=+16%2F7



 a%5B20%5D=+16%2F7+%2B%2819%29%2A20%2F7+=+396%2F7

Answer by rahulsoni001002(1) About Me  (Show Source):
You can put this solution on YOUR website!
T3=-8, T17=48 and T20=?
Tn=a+(n-1)d
T3=a+(3-1)d
-8=a+2d......(1)
Tn=a+(n-1)d
T17=a+(17-1)d
48=a+16d.....(2)
subtracting (2) from (1)
48=a+16d
-8=a+ 2d
- - -
____________
56= 14d
d=4
-8=a+2d putting d=4
-8=a+2(4)
-8=a+8
a=8+8
a=16
now a=16, d=4 ,T20=?
Tn=a+(n-1)d
T20=16+(20-1)(4)
=16+(19)(4)
=16+76
=92
T20=92