1. In {Achyranthes} (family Amaranthaceae), flowers are borne on an elongated, unbranched axis without pedicels, forming a spike inflorescence. Hence, Assertion (A) is true.
2. In a spike, flowers are arranged directly on the main axis (rachis) and it belongs to the {racemose type} of inflorescence. In racemose inflorescences, the floral buds open in an acropetal order — the older flowers are at the base and the younger ones are towards the apex.
3. The Reason (R) states that the spike shows a basipetal arrangement of sessile flowers, which is incorrect because basipetal succession occurs in {cymose (determinate)} inflorescences, not in racemose ones like spikes.
4. Therefore, while the Assertion (A) is true, the Reason (R) is false. Hence, the correct answer is (3) (A) is true, but (R) is false.