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\( u_{1}=q(4 p+1), u_{2}=q(2 p+3) \) and \( u_{3}=q(2 p-3) \) a) Find the value of \( p \) as an integer 1 The sum to infinity of the series is 250 . b) Find the value of \( q . \square I \)
Algebra Feb 15, 2025
The sum of the first \( n \) terms of a geometric series is denoted by \( S_{n} \) The common ratio of the series, \( r \), is greater than 1 . a) If \( S_{4}=5 S_{2} \) find the value of \( r \). b) Given further that \( S_{3}=21 \) determine the value of \( S_{10} \)
Algebra Feb 15, 2025
The first three terms of a geometric series are \( u_{1}=q(4 p+1), u_{2}=q(2 p+3) \) and \( u_{3}=q(2 p-3) \) a). Find the value of \( p \) as an integer The sum to infinity of the series is 250 . b) Find the value of \( q \).
Algebra Feb 15, 2025
Mimi is planning to save for the next 48 months in order to raise a deposit to buy a flat She plans to save \( \$ 300 \) this month and each successive month thereafter, to save an extra \( \$ 5 \) compared to the previous month. a) Find the amount she will save on the twelfth month. b) Find the total amount she will save at the end of the 48 months. Emmanuel is also planning to save for the next 48 months in order to buy a car. He plans to save \( \$ \) a this month and each successive month thereafter, to save an extra \( \$ 15 \) compared to the previous month. c) Find the value of \( a \), if Emmanuel saves the same amount of money as Anita does in the next 48 months.
Algebra Feb 15, 2025
Three consecutive terms of a geometric series are given in terms of a constant \( x \). \( U_{3}=(x+5), U_{4}=(4 x-1) \) and \( U_{5}=(2 x+3) \). Find the sum to infinity of the series. (Correct to four significant figures). Answer:
Algebra Feb 15, 2025
The first three terms of a geometric series are \( u_{1}=q(4 p+1), u_{2}=q(2 p+3) \) and \( u_{3}=q(2 p-3) \) a) Find the value of \( p \) as an integer The sum to infinity of the series is 250 . b) Find the value of \( q \).
Algebra Feb 15, 2025
Mimi is planning to save for the next 48 months in order to raise a deposit to buy a flat. She plans to save \( \$ 300 \) this month and each successive month thereafter, to save an extra \( \$ 5 \) compared to the previous month. a) Find the amount she will save on the twelfth month. b) )Find the total amount she will save at the end of the 48 months. Emmanuel is also planning to save for the next 48 months in order to buy a car. He plans to save \( \$ \) a this month and each successive month thereafter, to save an extra \( \$ 15 \) compared to the previous month. c) Find the value of \( a \), if Emmanuel saves the same amount of money as Anita does in the next 48 months. :
Arithmetic Feb 15, 2025
The first term of an arithmetic series is 51 and the eighth term is 100 . a) Find the twentieth term of the series. b) Determine the sum of the first twenty terms of the series.
Arithmetic Feb 15, 2025
The sum of the first \( n \) terms of a geometric series is denoted by \( S_{n} \). The common ratio of the series, \( r \), is greater than 1. a) If \( S_{4}=5 S_{2} \) find the value of \( r \). b) Given further that \( S_{3}=21 \) determine the value of \( S_{10} \).
Algebra Feb 15, 2025
\[ f(x) = 3x + 4 \quad g(x) = 2x - 3 \] \[ \text{Find: } f \circ g(x) \]
Algebra Feb 14, 2025
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