299,844 views
38 votes
38 votes
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.



User Marshally
by
3.2k points

1 Answer

26 votes
26 votes

Answer:

62

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.

User Tlenss
by
2.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.