Upbeat first-quarter results from heavyweights Shell and Tullow gave the UK oil and gas sector a shot in the arm on Tuesday, along with a takeover offer for Heritage Oil.First-quarter earnings were down 3% at Royal Dutch Shell, but well ahead of consensus estimates. Excluding large impairments on refineries in Asia and Europe which reflect "substantial" pressures on its Downstream business, earnings were $7.3bn. This was lower than the previous $7.5bn, but the figure still managed to smash the market's forecast of $5.1bn.The stock as 3% higher at 2,349p in afternoon trade.Tullow, meanwhile, confirmed that its full-year guidance remained at between 79,000 and 85,000 barrels of oil equivalent per day following a good performance since the start of the year. The company also announced an agreement to sell stakes in two North sea oil fields, farming down 53.1% of its Schooner unit interest and 60% of its Ketch asset to Faroe Petroleum.Prime Wealth Group labelled the stock as a 'buy', saying that the news marks a "turning point" for the shares after its recent weakness.The stock was up 1.7% at 880.5p.On the FTSE 250, the share price of Heritage Oil surged after the company announced that it had received a takeover offer from Energy Investments Global, part of Qatar's Al Mirqab Capital.Under the terms of the offer, which has been recommended by Heritage management, shareholders will receive 320p in cash for each share, a 25% premium to Tuesday's closing price of 255.6p. The offer values the company at £924m.Heritage also reported its full-year results which unveiled that profits doubled in 2013 on the back of record production from its flagship OML 30 lock in Nigeria.Others in the sector including Rockhopper Exploration, Afren and Cairn Energy were also rising strongly.Top performing sectors so far todayOil & Gas Producers 8,557.55 +1.77%Aerospace and Defence 4,777.95 +0.89%Industrial Transportation 3,084.02 +0.81%Software & Computer Services 1,181.37 +0.60%Food Producers & Processors 7,800.57 +0.58%Bottom performing sectors so far todayTechnology Hardware & Equipment 1,069.60 -2.58%Food & Drug Retailers 3,816.52 -2.28%Tobacco 38,777.64 -1.99%Health Care Equipment & Services 5,151.30 -1.35%Real Estate Investment Trusts 2,751.32 -1.28%BC