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Mathematics: AI SL

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Mathematics: AI SL

Available time 20 Minute(s)

Using sigma notation, write down an expression for the series.

Mountaineers are climing a cliff, where B represents its base and T its top.

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Available time 20 Minute(s)

01. Question

Level Medium

Maximum Mark 6

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Let $u_{n} = 5 n + 3,$ for $n \in ℤ^{+}$

(a). (i) Using sigma notation, write down an expression for $u_{1} + u_{2} + u_{3} + \dots + u_{20}$

[Marks: 2]

$\sum_{k = 1}^{20} (4 k + 1)$

$\sum_{k = 2}^{10} (4 k + 1)$

$\sum_{k = 1}^{20} 4 k$

$4 \sum_{k = 1}^{20} (k + 1)$

(ii) Find the value of the sum of the series.

[Marks: 2]

A geometric sequence is defined by $v_{n} = 5 \times 3^{n - 1},$ for $n \in ℤ^{+}$ .

(b). Find the value of the sum of the geometric series $\sum_{k = 1}^{10} v_{k}$ .

[Marks: 2]

End Test