Show that 28,23,18,13 ... , is arithmetic , .Hence find Un and the sum of the first n terms in the simplest form ??
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 -----> U
2 - U
1 = 23 - 28 = -5 or U
4 - U
3 = 13 - 18 = -5.
So now we just need to replace a = 28 and d = -5 in the formula ----> U
n = 28 + (n - 1)(-5) ---->
Un = 33 - 5nRequiem 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 ----> S
n = 0.5n(2(28) + (n-1)(-5))
Just simplify to get
Sn = 0.5n(61 - 5n) or
Sn = (61n - 5n2)/2
