Question

The 11th term of an arithmetic sequence is 32 and the sum of the first 11 terms is 187. Calculate the 21st term of the sequence.

Answer 1

Answer:

  62

Step-by-step explanation:

The general term of an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 +d(n -1)

The sum of n terms of an arithmetic sequence is ...

  Sn = (2·a1 +d(n -1))(n/2)

Using these relations and the given values of a11 and s11, we can find a1 and d:

  a11 = a1 +d(11 -1) = 32

  S11 = (2·a1 +d(11 -1))(11/2) = 187

These simplify to ...

  a1 +10d = 32

  2a1 +10d = 34 . . . . multiply the second equation by 2/11

__

Subtracting the first of these from the second, we get ...

  a1 = 2

Then the common difference is ...

  d = (32 -2)10 = 3

And the 21st term is ...

  a21 = 2 +3(21 -1) = 62

The 21st term is 62.