S and s (1 Viewer)

horndog huang 2 · Jan 6, 2016

Hello
I need help with this q
Suppose that Tn= ar^(n-1) is a gp with a limiting sum
Find the ratio if the sum of all terms except the first equals 5 times the first term

I started with Sn - T1=5T(1)
T(1)= a
Sn= 6a
But dont know where to go from there

Thanks

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InteGrand · Jan 6, 2016

horndog huang 2 said:
Hello
I need help with this q
Suppose that Tn= ar^(n-1) is a gp with a limiting sum
Find the ratio if the sum of all terms except the first equals 5 times the first term

I started with Sn - T1=5T(1)
T(1)= a
Sn= 6a
But dont know where to go from there

Thanks

Sent from my LG-D855 using Tapatalk

$Let the first term be $a$ and the common ratio be $r$. The second term is $ar$. So the sum of all terms except the first is $\frac{ar}{1-r}$ (limiting sum). This is given to be equal to $5a$. So we have$

$$\begin{align*} \frac{ar}{1-r} &= 5a \\ \Rightarrow \frac{r}{1-r}&= 5 \quad (\text{assuming } a\neq 0 \text{ so we can divide through by } a) \\ \Rightarrow r &= \frac{5}{6} \quad (\text{solving for }r). \end{align*}$

$Note that there is also a trivial G.P. with $a = 0$ and $r = 0$ that satisfies the given conditions.$

KingOfActing · Jan 7, 2016

InteGrand said:
$Let the first term be $a$ and the common ratio be $r$. The second term is $ar$. So the sum of all terms except the first is $\frac{ar}{1-r}$ (limiting sum). This is given to be equal to $5a$. So we have$

$$\begin{align*} \frac{ar}{1-r} &= 5a \\ \Rightarrow \frac{r}{1-r}&= 1 \quad (\text{assuming } a\neq 0 \text{ so we can divide through by } a) \\ \Rightarrow r &= \frac{1}{2} \quad (\text{solving for }r). \end{align*}$

$Note that there is also a trivial G.P. with $a = 0$ and $r = 0$ that satisfies the given conditions.$

You made a mistake in the second line, it should be equal to 5 not 1. The correct solution should be $r=\frac{5}{6}$

InteGrand · Jan 7, 2016

KingOfActing said:
You made a mistake in the second line, it should be equal to 5 not 1. The correct solution should be $r=\frac{5}{6}$

Oh yeah, whoops. Cheers!

S and s (1 Viewer)

horndog huang 2

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InteGrand

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KingOfActing

lukewarm mess

InteGrand

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