Question

If 10th term is 9 and 9th term is 10, then the common difference is
1) d=-2
2) d=-3
3) d=0
4) d=-1

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Answer 1

Answer:

a+9d=9

-(a+8d=10)

d= -1

fourth option is the right answer

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Answer 2

Need to FinD :-

• The common difference .

$\red{\frak{Given}}\begin{cases}\textsf{ 10th term of the AP is 9 .}\\\textsf{ 9th term of an AP is 10.} \end{cases}$

We can use the formula to find the nth term of a. AP .Let the first term of the AP be a and Common Difference be d .

• According to first Condition :-

$\sf:\implies T_n = a + (n-1)d \\\\\sf:\implies T_{10 }= a + (10-1)d \\\\\implies \boxed{\frak{ 9 = a + 9d }}\cdots\cdots (i)$

• According to second Condition :-

$\sf:\implies T_n = a + (n-1)d \\\\\sf:\implies T_{9}= a + (9-1)d \\\\\implies \boxed{\frak{ 10 = a + 8d }}\cdots\cdots (ii)$

$\rule{200}2$

• On subtracting the equations :-

$\sf:\implies T_9 - T_{10} = (a+8d) - (a+9d) \\\\\sf:\implies 10 - 9 = a + 8d - a -9d \\\\\sf:\implies 1 = -d\\\\\sf:\implies d =\dfrac{-1}{1} \\\\\sf:\implies \underset{\blue{\sf Option \ 4}}{\underbrace{\boxed{\pink{\frak{ Common \ Difference = (-1) }}}}}$