Question Number 21650 by Glorious Man last updated on 30/Sep/17
$${The}\:{three}\:{distinct}\:{successive}\:{terms}\:{of}\:{an}\:{A}.{P}\:{are} \\ $$$${the}\:{first},{second}\:{and}\:{fourth}\:{terms}\:{of}\:{a}\:{G}.{P}.\:{If}\:{the}\: \\ $$$${sum}\:{to}\:{infinity}\:{of}\:{a}\:{G}.{P}\:{is}\:\mathrm{3}+\sqrt{\mathrm{5}}\:,\:{find}\: \\ $$$${the}\:{first}\:{term}. \\ $$$$ \\ $$