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Hellllllllllllllllllllllllllllllllllllllllllp , Arithmetic Progression !!

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~HyDrOgEn~:
Show that 28,23,18,13 ... , is arithmetic , .Hence find Un and the sum of the first n terms in the simplest form ??

~HyDrOgEn~:
Hey golden girl  , it was really nice to meet you after  The IGCSE has finished , i appreciate that you are helping , but i didn't get it , can you please re Explain
thanks :D

The Golden Girl =D:
Nice to see you around too =D

I sent my friend a sg hopefully you'll find the answer later or perhaps by tomorrow =]

Freaked12:

--- Quote from: ~HyDrOgEn~ on December 20, 2010, 04:14:52 pm ---Show that 28,23,18,13 ... , is arithmetic , .Hence find Un and the sum of the first n terms in the simplest form ??

--- End quote ---

a+(n-1)d
 28+(n-1)-5
31-5n

second part

sum of first n numbers
n/2(2a+(n-1)d)
 n/2(2*28+(n-1)-5)
(-5n^2+61n)/ 2

Deadly_king:

--- Quote from: ~HyDrOgEn~ on December 20, 2010, 04:14:52 pm ---Show that 28,23,18,13 ... , is arithmetic , .Hence find Un and the sum of the first n terms in the simplest form ??

--- End quote ---

For the sequence to be an arithmetic progression it should fit in the equation Un = a + (n-1)d where a : First term, d : common difference and n : term number.

The sequence is arithmetic since the common difference is constant, i.e U1 - U2 = U3 - U4

So from the sequence we can not that the common difference is -5 -----> U2 - U1 = 23 - 28 = -5 or U4 - U3 = 13 - 18 = -5.

So now we just need to replace a = 28 and d = -5 in the formula ----> Un = 28 + (n - 1)(-5) ----> Un = 33 - 5n

Requiem made a little mistake there. ;)

Equation for the sum of n terms in an A.P = 0.5n(2a + (n - 1)d)

Again you just need to replace a = 28 and d = -5 ----> Sn = 0.5n(2(28) + (n-1)(-5))

Just simplify to get Sn = 0.5n(61 - 5n) or Sn = (61n - 5n2)/2

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