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Question Number 11261 Answers: 0 Comments: 0

The n^(th) term of a progression is np+q and the sum of n terms is denoted by S_n . Given that the 6^(th) term is 4 times 2^(nd) term and that S_3 =12, find the value of p and q. Express S_n in terms of n.

$$\mathrm{The}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{progression}\:\mathrm{is}\:\mathrm{np}+\mathrm{q}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{denoted}\:\mathrm{by}\:\mathrm{S}_{\mathrm{n}} . \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{6}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:\mathrm{4}\:\mathrm{times}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{term}\:\mathrm{and}\:\mathrm{that}\:\mathrm{S}_{\mathrm{3}} \:=\mathrm{12},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}. \\ $$$$\mathrm{Express}\:\mathrm{S}_{\mathrm{n}} \:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{n}. \\ $$

Question Number 11258 Answers: 1 Comments: 0

cos65=m ⇒ sin40=?

$${cos}\mathrm{65}={m}\:\:\Rightarrow\:{sin}\mathrm{40}=? \\ $$

Question Number 11256 Answers: 1 Comments: 0

In the arithmetic progression, u_(1 ) =1.Given that u_(7 ) , u_(11) and u_(17) are in geometric progression, find the value of each.

$$\mathrm{In}\:\mathrm{the}\:\mathrm{arithmetic}\:\mathrm{progression},\:\mathrm{u}_{\mathrm{1}\:} =\mathrm{1}.\mathrm{Given}\:\mathrm{that}\:\mathrm{u}_{\mathrm{7}\:} ,\:\mathrm{u}_{\mathrm{11}} \mathrm{and}\:\mathrm{u}_{\mathrm{17}} \:\mathrm{are}\:\mathrm{in}\:\mathrm{geometric}\: \\ $$$$\mathrm{progression},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{each}. \\ $$

Question Number 11255 Answers: 1 Comments: 0

If the sum of the first 4 terms of an A.P., is p, the sum of the first 8 terms is q and the sum of the first 12 terms is r, express (3p+r) in terms of q.

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{4}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}.,\:\mathrm{is}\:\mathrm{p},\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{8}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{q}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{12}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{r},\:\mathrm{express}\:\left(\mathrm{3p}+\mathrm{r}\right)\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{q}. \\ $$

Question Number 11249 Answers: 2 Comments: 0

x∈(0,2π) 2cos^2 x +sinx−1=0 ⇒Σx=?

$${x}\in\left(\mathrm{0},\mathrm{2}\pi\right) \\ $$$$\mathrm{2cos}^{\mathrm{2}} {x}\:+{sinx}−\mathrm{1}=\mathrm{0}\:\Rightarrow\Sigma{x}=?\: \\ $$

Question Number 11246 Answers: 2 Comments: 0

The sum of the first n terms of the series (1/2) + (3/4) + (7/8) + ((15)/(16)) + ... is equal to

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mathrm{3}}{\mathrm{4}}\:+\:\frac{\mathrm{7}}{\mathrm{8}}\:+\:\frac{\mathrm{15}}{\mathrm{16}}\:+\:...\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 11245 Answers: 1 Comments: 0

cos10×cos20×cos40=?

$${cos}\mathrm{10}×{cos}\mathrm{20}×{cos}\mathrm{40}=? \\ $$

Question Number 11228 Answers: 1 Comments: 0

Question Number 11238 Answers: 1 Comments: 0

f(1 − 2x) = g(x + 3) f^(−1) (x) = ? (A) 7 − 2g^(−1) (x) (B) 2g^(−1) (x) + 7 (C) 2g^(−1) (x) − 5 (D) 5 − 2g^(−1) (x)

$${f}\left(\mathrm{1}\:−\:\mathrm{2}{x}\right)\:=\:{g}\left({x}\:+\:\mathrm{3}\right) \\ $$$${f}^{−\mathrm{1}} \left({x}\right)\:=\:? \\ $$$$ \\ $$$$\left(\mathrm{A}\right)\:\mathrm{7}\:−\:\mathrm{2}{g}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left(\mathrm{B}\right)\:\mathrm{2}{g}^{−\mathrm{1}} \left({x}\right)\:+\:\mathrm{7} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{2}{g}^{−\mathrm{1}} \left({x}\right)\:−\:\mathrm{5} \\ $$$$\left(\mathrm{D}\right)\:\mathrm{5}\:−\:\mathrm{2}{g}^{−\mathrm{1}} \left({x}\right) \\ $$

Question Number 11221 Answers: 0 Comments: 4

Question Number 11146 Answers: 2 Comments: 0

∫sin^3 (1+2x)dx=....???

$$\int{sin}^{\mathrm{3}} \left(\mathrm{1}+\mathrm{2}{x}\right){dx}=....??? \\ $$

Question Number 11139 Answers: 1 Comments: 1

Question Number 11218 Answers: 0 Comments: 6

at tinkutara there are major bugs with combining brackets. e.g. typing: ∣A⟩=(∣B^∗ ⟩)^T writing ∣⟩(∣A)^∗ then changing it to ∣⟩(∣A)^∗ ⟩ causes odd size glitches. furthermore, while typing my previous post, a huge glitch occured where tapping the screen (moving the cursor?) caused the text to get really really big

$$\mathrm{at}\:\mathrm{tinkutara} \\ $$$$\: \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{major}\:\mathrm{bugs}\:\mathrm{with}\:\mathrm{combining} \\ $$$$\mathrm{brackets}. \\ $$$$\: \\ $$$$\mathrm{e}.\mathrm{g}.\:\mathrm{typing}: \\ $$$$\mid{A}\rangle=\left(\mid{B}^{\ast} \rangle\right)^{\mathrm{T}} \\ $$$$\: \\ $$$$\mathrm{writing}\:\mid\rangle\left(\mid{A}\right)^{\ast} \\ $$$$\mathrm{then}\:\mathrm{changing}\:\mathrm{it}\:\mathrm{to}\:\mid\rangle\left(\mid{A}\right)^{\ast} \rangle \\ $$$$\mathrm{causes}\:\mathrm{odd}\:\mathrm{size}\:\mathrm{glitches}. \\ $$$$ \\ $$$$\mathrm{furthermore},\:\mathrm{while}\:\mathrm{typing}\:\mathrm{my}\:\mathrm{previous} \\ $$$$\mathrm{post},\:\mathrm{a}\:\mathrm{huge}\:\mathrm{glitch}\:\mathrm{occured}\:\mathrm{where}\:\mathrm{tapping} \\ $$$$\mathrm{the}\:\mathrm{screen}\:\left(\mathrm{moving}\:\mathrm{the}\:\mathrm{cursor}?\right)\:\mathrm{caused} \\ $$$$\mathrm{the}\:\mathrm{text}\:\mathrm{to}\:\mathrm{get}\:\mathrm{really}\:\mathrm{really}\:\mathrm{big} \\ $$

Question Number 11145 Answers: 0 Comments: 1

let set S=R let nS={R, R, ..., R_(n sets of R) } n∈Z^+ is ∣S∣<∣nS∣? what if n=∣S∣?

$$\mathrm{let}\:\mathrm{set}\:{S}=\mathbb{R} \\ $$$$\mathrm{let}\:{nS}=\left\{\underset{{n}\:\mathrm{sets}\:\mathrm{of}\:\mathbb{R}} {\mathbb{R},\:\mathbb{R},\:...,\:\mathbb{R}}\right\}\:\:\:\:\:\:\:\:\:{n}\in\mathbb{Z}^{+} \\ $$$$\mathrm{is}\:\mid{S}\mid<\mid{nS}\mid? \\ $$$$\: \\ $$$$\mathrm{what}\:\mathrm{if}\:{n}=\mid{S}\mid? \\ $$

Question Number 11167 Answers: 2 Comments: 0

f(x)=ln∣x+(√((1+x^2 )))∣ is even or odd? give reasion.

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ln}\mid\mathrm{x}+\sqrt{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}\mid\:\mathrm{is}\:\mathrm{even}\:\mathrm{or}\:\mathrm{odd}?\: \\ $$$$\mathrm{give}\:\mathrm{reasion}. \\ $$

Question Number 11131 Answers: 0 Comments: 3

Proof with induction, for every n ∈ N Σ_(i = 1) ^n 2^(i + 2) = 2^(n + 3) − 8

$$\mathrm{Proof}\:\mathrm{with}\:\mathrm{induction},\:\mathrm{for}\:\mathrm{every}\:{n}\:\in\:\mathbb{N} \\ $$$$\underset{{i}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\:\mathrm{2}^{{i}\:+\:\mathrm{2}} \:=\:\mathrm{2}^{{n}\:+\:\mathrm{3}} \:−\:\mathrm{8} \\ $$

Question Number 11148 Answers: 1 Comments: 0

∫((x dx)/((x+1))^(1/3) )=....???