SOLUTION: The 49th term of an arithmetic progression is 23 and 62nd term is 37. What is the sum of first 110 terms of the series? Options 1) 3000 2) 3300 3) 3600

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Question 1024637: The 49th term of an arithmetic progression is 23 and 62nd term is 37. What is the sum of first 110 terms of the series?
Options
1) 3000
2) 3300
3) 3600
4) 3900

Found 2 solutions by rothauserc, robertb:
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
The nth term of an arithmetic progression is defined as
:
Xn = a + d(n-1), where a is the first term and n is the nth term number
:
We are given two equations
:
23 = a + d(49-1)
37 = a + d(62-1)
:
23 = a +48d
37 = a +61d
:
solve first equation for a
a = 23 - 48d
:
now substitute for a in second equation
:
37 = (23 -48d) +61d
13d = 14
d = 14/13
:
substitute for d in first given equation
:
23 = a + (14/13) * (48)
23 = a + 51.692307692
a = −28.692307692 approx -28.69
:
:
we want the sum of the first 110 terms, the sum of the first n terms of an arithmetic sequence is
:
Sn = (n/2)(2a + (n-1)d)
:
S110 = (110/2)(2(-28.69) + (109)(14/13))
S110 = (55)((−57.38) + 117.38)
S110 = (55)(60)
:
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S110 = 3300, answer is option 2
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Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website!