Math, asked by sajana833, 19 hours ago

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?​

Answers

Answered by itsRakesh
3

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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