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Sequences and Series

Question 6

A geometric series has first term $a\,$ and common ratio $r$ . The second term of the series is 4 and the sum to infinity of the series is 25.

Show that $25r^2 - 25r + 4 = 0$ .

[4]

Find the two possible values of $r$ .

[2]

Find the corresponding two possible values of $a$ .

[2]

Show that the sum, $S_n$ , of the first $n\,$ terms of the series is given by

S_n = 25(1 - r^n).

[2]

Given that $r\,$ takes the larger of its two possible values, find the smallest value of $n\,$ for which $S_n\,$ exceeds 24.

[4]

Markscheme

Sequences and Series Questions

A Level
Old Maths
Sequences and Series

9 exam-style questions on Edexcel A Level Old Maths Sequences and Series. Each one has a worked solution and a mark scheme showing where the marks go.

Sequences and Series

Question bank

Sequences and Series

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Question 6

A geometric series has first term $a\,$ and common ratio $r$ . The second term of the series is 4 and the sum to infinity of the series is 25.

Show that $25r^2 - 25r + 4 = 0$ .

[4]

Find the two possible values of $r$ .

[2]

Find the corresponding two possible values of $a$ .

[2]

Show that the sum, $S_n$ , of the first $n\,$ terms of the series is given by

S_n = 25(1 - r^n).

[2]

Given that $r\,$ takes the larger of its two possible values, find the smallest value of $n\,$ for which $S_n\,$ exceeds 24.

[4]

Markscheme

Sequences and Series Questions

A Level
Old Maths
Sequences and Series

9 exam-style questions on Edexcel A Level Old Maths Sequences and Series. Each one has a worked solution and a mark scheme showing where the marks go.