What is the first term if the last term ie 80 and The Sum Of The Firsts 10 Terms On Arithmetic Sequence Is 530?

In an arithmetic sequence, the sum of the first ( n ) terms can be calculated using the formula ( S_n = \frac{n}{2} (a + l) ), where ( S_n ) is the sum, ( n ) is the number of terms, ( a ) is the first term, and ( l ) is the last term. Given ( S_{10} = 530 ) and ( l = 80 ), we can set up the equation:

[ 530 = \frac{10}{2} (a + 80) ]

This simplifies to:

[ 530 = 5(a + 80) ]

Solving for ( a ), we find ( a + 80 = 106 ), leading to ( a = 26 ). Thus, the first term is 26.