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vovikov84 [41]
4 years ago
9

I am really struggling with this question. please help.

Mathematics
1 answer:
lakkis [162]4 years ago
8 0

Answer:

<h2><em>f</em><em>(</em><em>5</em><em>)</em><em>=</em><em>2</em><em>3</em></h2>

<em>Sol</em><em>ution</em><em>,</em>

<em>Here</em><em>,</em><em> </em><em>n</em><em>=</em><em>5</em><em> </em><em>which</em><em> </em><em>is</em><em> </em><em>x</em><em>></em><em>0</em>

<em>f</em><em>(</em><em>x</em><em>)</em><em>=</em><em>4</em><em>x</em><em>+</em><em>3</em>

<em> </em><em> </em><em> </em><em> </em><em>=</em><em>4</em><em>*</em><em>5</em><em>+</em><em>3</em>

<em> </em><em> </em><em> </em><em>=</em><em>2</em><em>0</em><em>+</em><em>3</em>

<em> </em><em> </em><em> </em><em>=</em><em>2</em><em>3</em>

<em>Hope</em><em> </em><em>this</em><em> </em><em>helps</em><em>.</em><em>.</em><em>.</em>

<em>Good</em><em> </em><em>luck</em><em> on</em><em> your</em><em> assignment</em><em>.</em><em>.</em>

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<h3><u>Solution:</u></h3>

Need to determine the sigma notation for the following sequence  

−10, −13, −16, …

Let's try to build a generic formula for given sequence  

The given sequence is in Arithmetic progression where first term = -10 and common difference = -3

<em><u>The formula for arithmetic progression is given as:</u></em>

a_n = a_1 + (n - 1)d

Where,

a_n is the nth term in the sequence

a_1 is the first term in the sequence

d is the common difference between the terms

Here in this sequence a_1 = -10 and d = -3

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\begin{array}{l}{\text { For } \mathrm{n}=1, \text { term is }-(3 \times 1+7)=-10} \\\\ {\text { For } \mathrm{n}=2, \text { term is }-(3 \times 2+7)=-13} \\\\ {\text { For } \mathrm{n}=3, \text { term is }-(3 \times 3+7)=-16}\end{array}

And so on

<em><u>Using sigma notation for arithmetic sequence:</u></em>

\sum_{k=1}^{n} a_{k}

So for first six terms value of n will vary from 1 to 6 and in sigma notation it can be represented as

\sum_{n=1}^{6}-(3 n+7)

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