Question

How do you find the first term of the arithmetic sequence given Sn = 781, d = 3, n = 22?

Answer 1

The first term is `a_1=4`

Explanation:

In this sequence we know the sum of 22 terms, the difference and we have to calculate the first term. We will use the formula for the sum of n terms:

`S_n=(a_1+a_n)/2*n` (1)

In this formula we have all data except `a_1`, which we want to find, and `a_n`, but the last term can be calculated using:

`a_n=a_1+(n-1)*d` (2)

When we substitute (2) to (1) we get:

`S_n=(2a_1+(n-1)*d)/2*n`

Now we can substitute given data and calculate `a_1`

`781=(2a_1+21*3)/2*22`

`781=(2a_1+63)*11`

`71=2a_1+63`
`2a_1=71-63`
`2a_1=8`
`a_1=4`