Final answer:
To find the value of a1 in the sequence, we can set up equations representing the relationship between each number. Then, using the given information, we can solve for a1. In this case, a1 is equal to 10/3.
Step-by-step explanation:
To find the value of a1, we can use the information given in the problem. We know that each number is twice the preceding number, so we can set up an equation to represent this relationship:
a2 = 2*a1
Similarly, we can write equations for the other numbers in the sequence:
a3 = 2*a2
a4 = 2*a3
And so on. Now, let's use the given information that a5 - a1 = 20. Substituting the expressions for a5 and a1 in terms of a2 gives us:
2*a4 - 2*a1 = 20
Simplifying this equation, we get:
2*2*a3 - 2*a1 = 20
4*a2 - 2*a1 = 20
Now, we can substitute the expression for a2 in terms of a1 to solve for a1.
4*(2*a1) - 2*a1 = 20
Simplifying this equation, we get:
8*a1 - 2*a1 = 20
6*a1 = 20
a1 = 20/6
a1 = 10/3