An arithmetic sequence has a 2nd term equal to 7 and 8th term equal to -23. Find the term of the sequence that has value -183
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Given:
a2 = 7
a8 = -23
an = -183
To find:
Term of the sequence that has value -183.
Solution:
Since, a2 = 7
=> a+(2-1)d = 7
=> a+d = 7 ---------------(1)
Also, given a8 = -23
=> a+(8-1)d = -23
=> a+7d = -23
Now, from (1) We get
a = 7-d ----------------(2)
Putting the value of a in the above equation
We get, (7-d)+7d = -23
=> 7-d+7d = -23
=> 7+6d = -23
=> 6d = -23-7
=> 6d = -30
=> d = -30/6
=> d = -5
Now, putting the value of d in equation (2)
We get, a = 7-(-5)
=> a = 7+5
=> a = 12
Now, an = -183
=> a+(n-1)d = -183
Putting values, We get
12+(n-1)(-5) = -183
=> -5n+5 = -183-12
=> -5n+5 = -195
=> -5n = -195-5
=> -5n = -200
=> n = -200/-5
=> n = 40
Hence, the 40th term of the given A.P. is -183.
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