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nth Term of A.P

If an is the ...

Question

If $a_{n}$ is the $n^{th}$ of an A.P. such that $a_{2} + a_{7} - a_{4} = 11$ and $a_{3} + a_{8} = 24,$ then

commom difference is

2

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first term is

2

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a_{7} = 14

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a_{10} = 21

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Solution

The correct options are
A commom difference is $2$
D $a_{10} = 21$
Let $a_{1} = a$ and common difference be $d$ ,
Now,
$a_{2} + a_{7} - a_{4} = 11 \Rightarrow (a + d) + (a + 6 d) - (a + 3 d) = 11 \Rightarrow a + 4 d = 11 \dots (1)$

$a_{3} + a_{8} = 24 \Rightarrow (a + 2 d) + (a + 7 d) = 24 \Rightarrow 2 a + 9 d = 24 \dots (2)$

By solving both the equations, we get :
$a = 3, d = 2 ∴ a_{7} = 3 + 6 \times 2 = 15 ∴ a_{10} = 3 + 9 \times 2 = 21$

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