Question

In an Ap the nth trrm is 1/m and mth term is 1/n.Find (i) (mn)th term (ii) sum of first (mn)terms​

Answer 1

$[tex]3x - 5y - 4 = 0 \\ take \: x \: as \: 1 \: 2 \: \: \: 3 \: and \: 0$

1st x as 0

$3(0) - 5y - 4 = 0 \\ - 5y = 4 \\ y = \frac{4}{ - 5}$

2nd x as 1

$3(1) - 5y - 4 = 0 \\ 3 - 4 - 5y = 0 \\ - 1 - 5y = 0 \\ - 5y = 1 \\ y = \frac{1}{ - 5}$

3rd x as 2

$3(2) - 5y - 4 = 0 \\ 6 - 4 - 5y = 0 \\ 2 - 5y = 0 \\ - 5y = - 2 \\ y = \frac{2}{5}$

now last x as 3

$3(3) - 5y - 4 = 0 \\ 9 - 4 - 5y = 0 \\ 5 - 5y = 0 \\ - 5y = - 5 \\ y = \frac{5}{5} \\ y = 1$

now 2nd eqution

$2y + 7 = 9x \\ 2y + 7 - 9x = 0 \\ \\ \\ take \: x \: as \: 0 \: \: 1 \: \: 2 \: \: and \: 3$

1st x as 0

$2y + 7 - 9(0) = 0 \\ 2y + 7 = 1 \\ 2y = - 7 \\ y = \frac{ - 7}{2}$

2nd x as 1

$2y + 7 - 9(1) = 0 \\ 2y + 7 - 9 = 0 \\ 2y - 2 = 0 \\ y = 1$

3rd x as 2

$2y + 7 - 9(2) = 0 \\ 2y + 7 - 18 = 0 \\ 2y - 11 = 0 \\ 2y = 11 \\ y = \frac{11}{2}$

4th x as 3

$2y + 7 - 9(3) = 0 \\ 2y + 7 - 27 = 0 \\ 2y = 20 \\ y = \frac{20}{2} \\ y = 2$

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Answer 2

HEY MATE

$<font color="blue"><marquee behavior="alternate">HERE IS YOUR ANSWER</marquee></font>$

3x−5y−4=0

takexas123and0

1st x as 0

\begin{lgathered}3(0) - 5y - 4 = 0 \\ - 5y = 4 \\ y = \frac{4}{ - 5}\end{lgathered}

3(0)−5y−4=0

−5y=4

y=

−5

4

2nd x as 1

\begin{lgathered}3(1) - 5y - 4 = 0 \\ 3 - 4 - 5y = 0 \\ - 1 - 5y = 0 \\ - 5y = 1 \\ y = \frac{1}{ - 5}\end{lgathered}

3(1)−5y−4=0

3−4−5y=0

−1−5y=0

−5y=1

y=

−5

1

3rd x as 2

\begin{lgathered}3(2) - 5y - 4 = 0 \\ 6 - 4 - 5y = 0 \\ 2 - 5y = 0 \\ - 5y = - 2 \\ y = \frac{2}{5}\end{lgathered}

3(2)−5y−4=0

6−4−5y=0

2−5y=0

−5y=−2

y=

5

2

now last x as 3

\begin{lgathered}3(3) - 5y - 4 = 0 \\ 9 - 4 - 5y = 0 \\ 5 - 5y = 0 \\ - 5y = - 5 \\ y = \frac{5}{5} \\ y = 1\end{lgathered}

3(3)−5y−4=0

9−4−5y=0

5−5y=0

−5y=−5

y=

5

5

y=1

now 2nd eqution

\begin{lgathered}2y + 7 = 9x \\ 2y + 7 - 9x = 0 \\ \\ \\ take \: x \: as \: 0 \: \: 1 \: \: 2 \: \: and \: 3\end{lgathered}

2y+7=9x

2y+7−9x=0

takexas012and3

1st x as 0

\begin{lgathered}2y + 7 - 9(0) = 0 \\ 2y + 7 = 1 \\ 2y = - 7 \\ y = \frac{ - 7}{2}\end{lgathered}

2y+7−9(0)=0

2y+7=1

2y=−7

y=

2

−7

2nd x as 1

\begin{lgathered}2y + 7 - 9(1) = 0 \\ 2y + 7 - 9 = 0 \\ 2y - 2 = 0 \\ y = 1\end{lgathered}

2y+7−9(1)=0

2y+7−9=0

2y−2=0

y=1

3rd x as 2

\begin{lgathered}2y + 7 - 9(2) = 0 \\ 2y + 7 - 18 = 0 \\ 2y - 11 = 0 \\ 2y = 11 \\ y = \frac{11}{2}\end{lgathered}

2y+7−9(2)=0

2y+7−18=0

2y−11=0

2y=11

y=

2

11

4th x as 3

\begin{lgathered}2y + 7 - 9(3) = 0 \\ 2y + 7 - 27 = 0 \\ 2y = 20 \\ y = \frac{20}{2} \\ y = 2\end{lgathered}

2y+7−9(3)=0

2y+7−27=0

2y=20

y=

2

20

y=2

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