It is known that the sum of the first n terms of the equal ratio sequence {an} is Sn, and A3 = 2, S3 = 32, find A6

It is known that the sum of the first n terms of the equal ratio sequence {an} is Sn, and A3 = 2, S3 = 32, find A6

Let the first term of the equal ratio sequence {an} be A1, and the common ratio be Q. from the meaning of the question, we can get S3 = A1 (1 + Q + Q2) = 32, ①, A3 = a1q2 = 2 & nbsp; ②, ① △ ②, we can get 1 + Q + q2q2q2 = 34, simplify Q2 + 4q + 4 = 0, and get q = - 2, ｜ A6 = A3 · Q3 = 2 · (- 2) 3 = - 16

It is known that the sum of the first n terms of the equal ratio sequence {an} is Sn, and A3 = 2, S3 = 32, find A6

Let the first term of the equal ratio sequence {an} be A1, and the common ratio be Q. from the meaning of the question, we can get S3 = A1 (1 + Q + Q2) = 32, ①, A3 = a1q2 = 2 & nbsp; ②, ① △ ②, we can get 1 + Q + q2q2q2 = 34, simplify Q2 + 4q + 4 = 0, and get q = - 2, ｜ A6 = A3 · Q3 = 2 · (- 2) 3 = - 16

It is known that the sum of the first n terms of the equal ratio sequence {an} is SN. If A3 = 32 and S3 = 92, then the value of A1 is SN______ ．

Let the first term of the equal ratio sequence {an} be A1, and the common ratio be Q. if q = 1, from A3 = A1 = 32s3 = 3A1 = 92, A1 = 32 is obtained. If Q ≠ 1, then A3 = a1q2 = 32 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; ① S3 = A1 (1 − Q3) 1 − q = 92 & nbsp; ②, from ①, A1 = 32q2, substituting ②, q = − 12, substituting ①, A1 = 6, so the value of A1 is 32 or 6. Therefore, the answer is 32 or 6