Three numbers $a , a + b , 2 a - b$ form an arithmetic sequence in this order, and three numbers $1 , a - 1, 3 b + 1$ form a geometric sequence with positive common ratio in this order. Find the value of $a ^ { 2 } + b ^ { 2 }$. [3 points]
Three numbers $a , a + b , 2 a - b$ form an arithmetic sequence in this order, and three numbers $1 , a - 1, 3 b + 1$ form a geometric sequence with positive common ratio in this order. Find the value of $a ^ { 2 } + b ^ { 2 }$. [3 points]