Question

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?​

Answer 1

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