+0

# Arithmetic sequence

0
181
2

first 3 terms of arithmetic sequence where the 21st term is -38 and the 50th term is -125

Guest May 7, 2017
Sort:

#1
+91239
+2

first 3 terms of arithmetic sequence where the 21st term is -38 and the 50th term is -125

a+20d=-38

a+49d=-125

now solve simultaneously.

Melody  May 7, 2017
#2
+18777
0

first 3 terms of arithmetic sequence

where the 21st term is -38 and the 50th term is -125

Let
$$\begin{array}{ll} x=21 & t_x=t_{21}=-38 \\ y=50 & t_y=t_{50}=-125 \\ z=1 & t_z=t_1= ? \\ \end{array}$$

$$\begin{array}{|lrcll|} \hline \text{AP:} &\mathbf{ t_z } &\mathbf{=}& \mathbf{ t_x\cdot (\frac{z-y}{x-y}) +t_y\cdot (\frac{x-z}{x-y}) } \\ &t_{1} &=& (-38)\cdot (\frac{1-50}{21-50}) + (-125)\cdot (\frac{21-1}{21-50}) \\ &t_{1} &=& (-38)\cdot (\frac{-49}{-29}) + (-125)\cdot (\frac{20}{-29}) \\ &t_{1} &=& -38\cdot (\frac{49}{29}) + 125\cdot (\frac{20}{29}) \\ &t_{1} &=& \frac{-38\cdot 49+ 125\cdot 20}{29} \\ &t_{1} &=& \frac{638}{29} \\ & \mathbf{ t_{1} } & \mathbf{=} & \mathbf{22} \\ \hline \end{array}$$

Let
$$\begin{array}{ll} x=21 & t_x=t_{21}=-38 \\ y=50 & t_y=t_{50}=-125 \\ z=2 & t_z=t_2= ? \\ \end{array}$$

$$\begin{array}{|lrcll|} \hline \text{AP:} &\mathbf{ t_z } &\mathbf{=}& \mathbf{ t_x\cdot (\frac{z-y}{x-y}) +t_y\cdot (\frac{x-z}{x-y}) } \\ &t_{2} &=& (-38)\cdot (\frac{2-50}{21-50}) + (-125)\cdot (\frac{21-2}{21-50}) \\ &t_{2} &=& (-38)\cdot (\frac{-48}{-29}) + (-125)\cdot (\frac{19}{-29}) \\ &t_{2} &=& -38\cdot (\frac{48}{29}) + 125\cdot (\frac{19}{29}) \\ &t_{2} &=& \frac{-38\cdot 48+ 125\cdot 19}{29} \\ &t_{2} &=& \frac{551}{29} \\ & \mathbf{ t_{2} } & \mathbf{=} & \mathbf{19} \\ \hline \end{array}$$

$$\begin{array}{|lrcll|} \hline d&=&t_2-t_1 \\ d&=&19-22 \\ d&=&-3 \\\\ t_3 &=& t_2 +d \\ t_3 &=& 19-3 \\ \mathbf{ t_{3} } & \mathbf{=} & \mathbf{16} \\ \hline \end{array}$$

The first 3 terms of arithmetic sequence: 22, 19, 16, ...

heureka  May 8, 2017
edited by heureka  May 8, 2017

### 6 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details