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

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Answer 1 · 2015-07-05T09:07:26

The first term is $a_1=4$

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 $a_1$

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

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

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