$$\underset{\,\,\,\,{\textcolor[rgb]{0.66,0.66,0.66}{\rightarrow {\mathtt{in, an, arithmetic, sequence, and, find}}}}}{{solve}}{\left(\begin{array}{l}{\mathtt{In}}={\mathtt{0}}\\

{\mathtt{an}}={\mathtt{0}}\\

{\mathtt{arithmetic}}={\mathtt{0}}\\

{\mathtt{sequence}}={\mathtt{0}}\\

{t}{\left({\mathtt{8}}\right)}={\mathtt{0}}\\

\mathrm{ERROR}={\mathtt{145}}\\

{\mathtt{and}}={\mathtt{0}}\\

{t}{\left({\mathtt{50}}\right)}={\mathtt{0}}\\

\mathrm{ERROR}={\mathtt{607}}\\

{\mathtt{Find}}={\mathtt{0}}\\

\mathrm{ERROR}={\mathtt{0}}\end{array}\right)}$$

Guest Jul 25, 2015

#1**+10 **

Arithmetic sequence is t(n) = a + (n-1)*d where a is the first term, d is the difference and t(n) is the n'th term

So:

145 = a + 7d from the 8'th term

607 = a + 49d from the 50'th term

Subtract the first equation from the second

462 = 42d

d = 462/42 = 11

Substitute this back into the first equation

145 = a + 7*11

a = 145 - 77 = 68

Hence t(129) = 68 + 128*11 = 1476

.

Alan
Jul 25, 2015

#1**+10 **

Best Answer

Arithmetic sequence is t(n) = a + (n-1)*d where a is the first term, d is the difference and t(n) is the n'th term

So:

145 = a + 7d from the 8'th term

607 = a + 49d from the 50'th term

Subtract the first equation from the second

462 = 42d

d = 462/42 = 11

Substitute this back into the first equation

145 = a + 7*11

a = 145 - 77 = 68

Hence t(129) = 68 + 128*11 = 1476

.

Alan
Jul 25, 2015

#2**+5 **

please help !!! In an arithmetic sequence, t(8) = 145 and t(50) = 607. Find t(129).

$$\small{\text{$

\begin{array}{lrcl}

& t_8 = a+(8-1)d &=& a+7d \\

& t_{50} =a + (50-1)d &=& a+49 d\\

\\

(1) & \dfrac{ t_{50}+t_8 }{2} &=& a + 28d \\

\\

& t_{50}-t_8 &=& 42d \\

(2) & ( t_{50}-t_8 )\cdot \dfrac{100}{42} &=& 100d\\

\\

& t_{129} &=& a + (129-1)d \\

& t_{129} &=& a + 128d \\

& t_{129} &=& a + 28d + 100d \qquad | \qquad a + 28d = \dfrac{ t_{50}+t_8 }{2} \qquad 100d =( t_{50}-t_8 )\cdot \dfrac{100}{42} \\

& t_{129} &=& \dfrac{ t_{50}+t_8 }{2} + ( t_{50}-t_8 )\cdot \dfrac{100}{42}\\\\

& t_{129} &=& \dfrac{607+145}{2} + (607-145)\dfrac{100}{42}\\\\

& t_{129} &=& 376 + 1100 \\

&\mathbf{ t_{129} }& \mathbf{=} & \mathbf{ 1476 }\\

\end{array}

$}}$$

heureka
Jul 27, 2015