Question 354971: yes! i need help with this problem the sum of two consecutive terms in the arithmetic sequence 1,4,7,10,,, is 299 find these two terms? thank you!
Found 3 solutions by stanbon, robertb, jrfrunner:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The sum of two consecutive terms in the arithmetic
sequence 1,4,7,10,,, is 299 find these two terms?
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a(1) = 1
d = 4-1 = 3
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Two consecutive terms would be:
a(n) = a(1)+(n-1)d
a(n+1) = a(1)+(n)d
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Equation:
1 + (n-1)3 + 1+3n = 299
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2 + 3n-3 + 3n = 299
6n = 300
n = 50
n+1 = 51
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a(50) = 1 + 49*3 = 148
a(51) = 148+3 = 151
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Check:
148+151 = 299
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cheers,
Stan H.
Answer by robertb(5830)  (Show Source):
You can put this solution on YOUR website!
asubn = asub1 + (n-1)d
asub(n+1) = asub1 + nd.
Adding corresponding sides,
asubn + asub(n+1) = 2asub1 + (2n-1)d.
then
299 = 2asub1 + (2n-1)d
299 = 2*(1) + (2n-1)*3
299 = 2 + (2n-1)3
297 = (2n-1)3
99 = 2n-1
100 = 2n
n = 50.
so its the 50th term (148) and the 51st term (151).
Answer by jrfrunner(365)  (Show Source):
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