A-Level Edexcel Maths Pure Graphs of Functions: A sequence $u_1, u_2, u

A sequence $u_1, u_2, u_3, ...$ satisfies t_{n+1} = 2u_n - 1, ext{ for } n > 1 Given that $u_2 = 9$, a) find the value of $u_1$, and the value of $u_4$, b) evaluate $\\sum_{r=1}^4 u_r$. - Edexcel - A-Level Maths Pure - Question 6 - 2013 - Paper 3

Question 6

$A-sequence-$u_1,-u_2,-u_3,-...$-satisfies--t_{n+1}-=-2u_n---1,--ext{-for-}-n->-1--Given-that-$u_2-=-9$,--a)-find-the-value-of-$u_1$,-and-the-value-of-$u_4$,--b)-evaluate-$\\sum_{r=1}^4-u_r$.-Edexcel-A-Level Maths Pure-Question 6-2013-Paper 3.png$

A sequence $u_1, u_2, u_3, ...$ satisfies t_{n+1} = 2u_n - 1, ext{ for } n > 1 Given that $u_2 = 9$, a) find the value of $u_1$, and the value of $u_4$, b) eval... show full transcript

Worked Solution & Example Answer:A sequence $u_1, u_2, u_3, ...$ satisfies t_{n+1} = 2u_n - 1, ext{ for } n > 1 Given that $u_2 = 9$, a) find the value of $u_1$, and the value of $u_4$, b) evaluate $\\sum_{r=1}^4 u_r$. - Edexcel - A-Level Maths Pure - Question 6 - 2013 - Paper 3

Step 1

find the value of $u_1$, and the value of $u_4$

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Answer

To find $u_1$ , we can use the given equation:

$u_{n+1} = 2u_n - 1$

Starting with $n=2$ :

$u_3 = 2u_2 - 1 = 2(9) - 1 = 17$

Now, applying it again to find $u_4$ :

$u_4 = 2u_3 - 1 = 2(17) - 1 = 33$

Thus, the values are:

$u_1 = 17$
$u_4 = 33$

Step 2

evaluate $\sum_{r=1}^4 u_r$

99%

104 rated

Answer

Now, we evaluate the sum:

$\sum_{r=1}^4 u_r = u_1 + u_2 + u_3 + u_4$

We already have:

$u_1 = 17$
$u_2 = 9$
$u_3 = 17$
$u_4 = 33$

So,

$\sum_{r=1}^4 u_r = 17 + 9 + 17 + 33 = 76$

Therefore, the evaluation gives us $76$ .

A sequence $u_1, u_2, u_3, ...$ satisfies t_{n+1} = 2u_n - 1, ext{ for } n > 1 Given that $u_2 = 9$, a) find the value of $u_1$, and the value of $u_4$, b) evaluate $\\sum_{r=1}^4 u_r$. - Edexcel - A-Level Maths Pure - Question 6 - 2013 - Paper 3

Worked Solution & Example Answer:A sequence $u_1, u_2, u_3, ...$ satisfies t_{n+1} = 2u_n - 1, ext{ for } n > 1 Given that $u_2 = 9$, a) find the value of $u_1$, and the value of $u_4$, b) evaluate $\\sum_{r=1}^4 u_r$. - Edexcel - A-Level Maths Pure - Question 6 - 2013 - Paper 3

find the value of $u_1$, and the value of $u_4$

evaluate $\sum_{r=1}^4 u_r$

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