SOLUTION: The first and second terms of an arithmetic sequence are a and b respectively. If the nth term is c, express n in terms of a b and c and hence find the sum of these n terms.

Question 1124987: The first and second terms of an arithmetic sequence are a and b respectively. If the nth term is c, express n in terms of a b and c and hence find the sum of these n terms.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The first term is a; the second is b; so the common difference is (b-a).

The n-th term is then the first term plus the common difference (n-1) times:

<-- answer to the first question

The sum of the series is (number of terms) times (average of first and last terms):

<-- answer to the second question

Let's check these formulas with an example -- just in case we made an error in our algebra....

a = 3; b = 5; 9 terms.

The common difference is b-a = 2; the 9th term, c, is 3+8(2) = 19.

We know the number of terms is 9; our formula says the number of terms should be

Our formula gives the right result for this example.

The sum of the series is .

Our formula says the sum is supposed to be

Our formula for the sum also gives the right result for this example.
RELATED QUESTIONS
In an arithmetic sequence, the mth and nth term are n and m, respectively. What is its... (answered by stanbon)

The ninth and seventeenth terms of an arithmetic sequence are negative 8 and 32,... (answered by ikleyn,rothauserc,greenestamps)

The first term of an arithmetic progression is 12 and the sum of the first 16 terms is... (answered by greenestamps)

When the terms of a Geometric Progression(G.P) with common ratio r=2 is added to the... (answered by greenestamps,jim_thompson5910)

if the first term of a geometric sequence is 3/2 and the second and third terms are -3/4... (answered by stanbon)

4. In an arithmetic sequence, the first term is 3 and the second term is 7. a. Find the (answered by Boreal)

The second and fifth terms of an arithmetic sequence are 17 and 19, respectively. What is (answered by Theo)

Here are the first 5 terms of a arithmetic sequence 7 10 13 16 19 What is an expressiom... (answered by stanbon)

the sum of the second and sixth terms of an arithmetic sequence is 4. the third term is... (answered by Fombitz)