Arithmetic series..... Log.. other problems..

**An arithmetic series has five term a and common difference d.**

The sum of the first 31 terms of the series is 310.

**a)** Show that a + 15d = 10

*> S31 = 31/2 ( 2a + (31-1) d)*

> 31( a + 15d ) = 310

> a + 15d = 310/31; a + 15d = 10(Rock)

**b)**Given also that the 21st term is twise the 16th term, find the value of d.

???

**c)**the nth term of the series is un. Given that

K

Sum un = 0, find the value of K.

n = 1

???

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**Find the value of x in each of the following:**

**(A)**. log9x = 0

**(B)**. log9x = 1/2

of coz i noe how to do it on the calculator with the answers 1 for **(A)** and 3 for **(B)**, but how do i get it withour a calculator??

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**A curve has equation y = 1/x^3 + 48x.**

**a)** Find dy/dx.

*>> dy/dx = 3x^-4 + 48*

**b)** Hence find the equation of each of the two tangents to the curve that are parallel to the x-axis.

*>> -3x^-4 + 48 = 0*

>> x^-4 = 16

>> x = +-1/2

**c)** Find the equation of the normal to the curve at the point (1,49)

???????????(Angry)