Question

Find A8 for the geometric series with r=2, S8=1020, A1=4

Answer 1

To find A8 for the geometric series with r=2, A1=4, and S8=1020, we use the property A8 = A1 * r^7. By substituting the values, we get A8 = 4 * 2^7 which equals 512.

Step-by-step explanation:

To find the eighth term, A8, of the geometric series given the common ratio r=2, the first term A1=4, and the sum of the first eight terms S8=1020, we can use the formula for the sum of a geometric series: Sn = A1 * (1 - rn) / (1 - r), where Sn is the sum of the first n terms, A1 is the first term, r is the common ratio, and n is the number of terms.

To isolate A8, we note that A8 = A1 * r7 because each term is the previous term multiplied by the common ratio r. Substituting the given values:

• A8 = 4 * 27
• A8 = 4 * 128
• A8 = 512

Therefore, the eighth term of the geometric series is 512.

Answer 2

a8=512

Goodluck--hope this helps