a¹=100,r=½
The given information states that a¹ is equal to 100 and r is equal to ½.
To find the value of a², we need to use the formula for the nth term of a geometric sequence, which is given by:
an = a₁ * r^(n-1)
Here, "an" represents any term in the sequence, "a₁" is the first term, "r" is the common ratio, and "n" is the term number.
In this case, we want to find a², which means we need to substitute "n = 2" into the formula. Let's do that:
a² = a₁ * r^(2-1)
Since a¹ is given as 100 and r is given as ½, we can substitute these values into the formula:
a² = 100 * (½)^(2-1)
Simplifying further:
a² = 100 * (½)^1
The exponent of 1 in this case does not affect the value of ½, so we have:
a² = 100 * ½
Multiplying 100 by ½:
a² = 50
Therefore, a² is equal to 50.