In the equal ratio sequence {an}, the sum of the first n terms is SN. If SM, SM + 2, SM + 1 are equal difference sequence, then am, am + 2, am + 1 are equal difference sequence. (1) write the inverse proposition of this proposition; (2) judge whether the inverse proposition is true? The proof is given

In the equal ratio sequence {an}, the sum of the first n terms is SN. If SM, SM + 2, SM + 1 are equal difference sequence, then am, am + 2, am + 1 are equal difference sequence. (1) write the inverse proposition of this proposition; (2) judge whether the inverse proposition is true? The proof is given

(1) In {an} {an}, the sum of the first n items is Sn, and if am, am + 2, am + 1 is an arithmetic sequence, then SM, SM + 2, SM + 1 is an arithmetic sequence. (2) the first item of {an} is A1, and the common ratio is Q. from the title, we know: 2am + 2 = am + am + 1, that is: 2am + 2 = am + am + 1, that is, if am, am, am + 2, am + 2, am + 2, am + 2, am + 2, am + 2, am + 1, am + 1, am + 1, am + 1, am + 2, am + 1 = 2 = A1, 2, 2 A1 = A1 \1; A1
A1
A1
A1
A1
A1
A1 \\1; aqaqaqaqaqaqm + 1) A1 When q = − 12, 2sm + 2 = 2A1 (1 − (− 12) m + 2) 1 + 12 = 43a1 [1 − (− 12) m + 2], SM + SM + 1 = A1 (1 − (− 12) m) 1 + 12 + 2A1 (1 − (− 12) m +) 1 + 12 = 43a1 [1 − (− 12) m + 2] - 2sm + 2 = SM + SM + 1, and the inverse proposition is true