6. The sum of first 11 terms of an arithmetic sequence is 235 and the sum of first 12 terms is 300. a) What is its 6 degrees term ? b) What is its 12 degrees term? c) What is its common difference? d) What is its algebraic form?
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Answer:
S11 = 235
S12 = 300
=> S12-S11 = 12th term = 300 - 235 = 65
T12 = a+11d = 65 => Equation1
S11 = (11/2)(2a + 10d) = 235 => Equation2
S12 = (12/2)(2a+11d) = 6(2a+11d) = 12a+66d = 300 => Equation3
Take equation 1 and 3 :
12a+66d=300
a+11d=65
By solving the 2 equations, we get:
a = -15 , and d = 80/11
So 1) 6th term = a+5d = 235/11
2) 12th term = a+11d = 65
3) Common difference (d) = 80/11
4) Algebraic form =>
Tn = -15 + (n-1)*(80/11), and
Sn = (n/2)(-30 + (n-1)(80/11))
Where Tn = Nth term
And Sn = Sum of Nth term
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