Find a12 when a1 = 5 and r = – 2.
I assume we're doing a G.P. here.
a12 = a1*r^11 = 5*(-2)^11 = ?
To find the value of a12 when a1 = 5 and r = -2, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
In this case, a1 = 5, r = -2, and we want to find a12.
So, we plug these values into the formula:
a12 = 5 * (-2)^(12-1)
Now, let's simplify the expression:
a12 = 5 * (-2)^11
To simplify further, we need to calculate (-2)^11. One way to do this is by repeatedly multiplying -2 by itself:
(-2)^11 = -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2 * -2
Now, multiplying these 11 factors of -2 together, we get:
(-2)^11 = -2048
So, substituting this value back into the original equation, we have:
a12 = 5 * (-2)^11 = 5 * (-2048) = -10,240
Therefore, the value of a12 when a1 = 5 and r = -2 is -10,240.