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Without Using A Calculator, Find The Value Of:: 16 Log 1 6 1 5 + 1 2 Log 2 5 2 4 + 7 Log 8 1 8 0 + Log (2)

The document contains 7 math questions about series and sequences, exponents, and logarithms: 1) Find the values of p and q given an expression for the sum of terms in an arithmetic sequence and the sums of the first 3 and 5 terms. Determine the nth term and common difference. 2) For an arithmetic sequence of 30 terms, where the sum of the even terms exceeds the odd terms by 8, find the common difference and an expression for the sum of the first n terms. 3) Express the recurring decimal 0.462 as a rational number using an infinite geometric series. 4) Find the values of x for which a geometric series with first two terms of x + 3 and x

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132 views2 pages

Without Using A Calculator, Find The Value Of:: 16 Log 1 6 1 5 + 1 2 Log 2 5 2 4 + 7 Log 8 1 8 0 + Log (2)

The document contains 7 math questions about series and sequences, exponents, and logarithms: 1) Find the values of p and q given an expression for the sum of terms in an arithmetic sequence and the sums of the first 3 and 5 terms. Determine the nth term and common difference. 2) For an arithmetic sequence of 30 terms, where the sum of the even terms exceeds the odd terms by 8, find the common difference and an expression for the sum of the first n terms. 3) Express the recurring decimal 0.462 as a rational number using an infinite geometric series. 4) Find the values of x for which a geometric series with first two terms of x + 3 and x

Uploaded by

raja_tanuku
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as ODT, PDF, TXT or read online on Scribd
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Question 1(Series & Sequences)

The sum Sn, of the first terms of an arithmetic sequence is given by Sn = pn + qn2. We are
given that S3 = 6 and S5 = 11. With this information,
a) Find the values of p and q,
b) Deduce an expression for the nth term and the value of the common difference.

Question 2 (Series & Sequences)


An arithmetic sequence of 30 terms is such that the sum of the even numbered terms exceeds
the sum of the odd numbers terms by 8. Find:
a) The common difference.
b) An expression for Sn, the sum of the first n terms.

Question 3 (Series & Sequences)


Use an infinite geometric series to express the recurring decimal 0.462 as a rational number.

Question 4 (Series & Sequences)


x + 3 and x -2 are the first two terms of a geometric series. Find the values of x for which the
series converges.

Question 5 (Exponents & Logarithms)


Solve the simultaneous equations:
e
√ e
x

¿
2 y
e

l o g4
( x + 2 )
− ¿
l o g2
( y )
¿
1

Question 6 (Exponents & Logarithms)


Without using a calculator, find the value of:
16
lo g ⁡
1 6
1 5( )
+ ¿ 1 2
lo g (
⁡
2 5
2 4 )
+ ¿ ¿ 7

log ⁡( 8 1
8 0 )
+ ¿ ¿ l og ⁡( 2 )

Question 7 (Exponents & Logarithms)


Solve the following:
l o g( 2 x + 3 )

( 6 x
2
+ 2 3 x + 21 )
¿
4
− ¿
l o g( 3 x + 7 )

( 4 x 2
+ 12 x + 9 )

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