1127-A. 1127-A: Fill & Download for Free

My long gone father owned a gas station, and once asked me the following question. I'm making up the numbers because I no longer remember the real ones."I changed the price of regular gas in the middle of the day today. The morning price was 1.29/gallon, the afternoon price 1.33/gallon. I know in total we sold 1127 gallons for $1470.47. How much did we sell at each price?"This is of course two linear equations in two unknowns, easily solved. It really impressed my father how quickly I did it. It left an impression on me as well: one of the few times algebra arose in real life.Unfortunately my father died shortly after I got out of graduate school and never really got to reap the benefits that his investment in my education wrought. Except a little bit when I solved two linear equations in two unknowns for him. I love you and I miss you dad; I wish you were still around.Edit: I suppose I should do the math.[math]m+a = 1127[/math][math]1.29m + 1.33a = 1470.47 [/math][math]m = [/math][math]1127-a[/math][math][/math][math]1.29(1127-a) + 1.33a = 1470.47[/math][math]1.29\cdot 1127 + (1.33-1.29)a = 1470.47[/math][math](1.33-1.29) a = 1470.47 - 1.29\cdot 1127[/math][math]a = \frac{ 1470.47 - 1.29\cdot 1127 } {1.33-1.29} [/math][math]a = 416[/math] gallons sold in the afternoon[math]m = 1127 - 416 = 711[/math] gallons sold in the morning.Check: [math]1.29 \cdot 711 + 1.33 \cdot 416 = 1470.47 \checkmark[/math]

Oh dear, now you've done it.Combat aircraft don't tend to stay in service for half a century if they've been swiftly abandoned and not improved on at all.What you refer to as the ‘Harrier Jump Jet’ began life as the Hawker P.1127, an experimental V/STOL test aircraft. The following is a great big list of Harrier variants in service with the RAF and Royal Navy - I've omitted the US variants on the basis that I don't know enough about ‘em.Hawker P.1127: Six were built, two initial prototypes and four further development aircraft.This project wasn't abandoned, and it was improved on.Next came the Hawker-Siddeley Kestrel. A further development of the P.1127 aircraft, and soon involved West Germany and the US for tests in a newly formed evaluation squadron.Hawker-Siddeley Kestrel FGA.1: Nine built, they differed slightly in parts and had minor design changes as they were built and tested.This wasn't abandoned, and it was improved on.The next step was a full production Harrier GR.1, ordered by the RAF. The first GR.1s didn't differ too much from the last Kestrels, but were the official RAF designation for the new aircraft.The Harrier GR.1 wasn't abandoned, and was improved on considerably.Hawker-Siddeley Harrier GR.1: 61 GR.1s built, 41 upgraded to GR.1A with 17 new builds.The Harrier GR.3 was the next step up, involving new laser trackers and radar warning receivers, along with an uprated Pegasus 11 engine. 40 were built and over 60 other GR.1 and 1As upgraded to GR.3 standard.The US also upgraded their 1st generation Harriers, with the AV-8A and AV-8C variants in service with the US Marine Corps.Now comes the Sea HarrierBritish Aerospace Sea Harrier FRS.1: 57 built, based largely on the preceding RAF GR.3, it had a different upper fuselage structure and nose to accommodate a new Blue Fox radar.Many of the FRS.1s built were upgraded to FA.2 standard, post-Falklands War. The FA.2 used the improved Blue Vixen radar and had the capability for more advanced missiles.The first generation of Harriers was, you guess it, improved and most definitely not abandoned.These improvements continued, and development of a vastly modernised design, a collaboration between the US and UK, producing the BAe/McDonnell-Douglas Harrier II.The Harrier GR.5 and later GR.5A were the first to enter service with the RAF. 62 of which were built. The US AV-8B Harrier II was externally similar but differed in avionics quite considerably.This was upgraded into the GR.7 and GR.7A - themselves later upgraded into the improved but ill-fated GR.9 and GR.9A.P.1127, Kestrel, Harrier GR.1, 1A, 3, 5, 5A, 7, 7A, 9, 9A, Sea Harrier FRS.1 and FA.2. Without the array of two seater variants. The US had AV-8A, C, B, B Plus and B Night Attack as their main combat variants.I've probably missed some, but you get the point - the Harrier was continually developed for half a century, very few aircraft can claim the same…

After looking at the series, a clear pattern can be seen.The second term,27=9*3.The third term 31 equals 27+4.The fourth term, 155, equals 31*5The fifth term, 161 equals the 155+6Finally, the sixth term, 1127 equals 161*7.This pattern can allow us to find a formula for the nth term.If n is even:The nth term equals the previous term multiplied by the nth odd number. For example, the second term, 27, equals the first term 9, multiplied by the 2nd odd number, 3.For odd n >=3:The nth term equals the previous term + (n+1) . For example, the third term, 31 equals 27+(3+1)=27+4Since the next term in the series is an odd numbered term(n=7), it equals 1127+(n+1) Substituting for n:T7=1127+(7+1)=1127+8=1135Hope this helped