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

1 Answer
Jul 5, 2015

Answer:

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#