Question

If the common defference of a AP is 3 than find the value of A11 - A12​

Answer 1

GIVEN :–

• Common difference of A.P. = 3

TO FIND :–

$\\ \sf {A}_{11} - {A}_{12} = ?$

SOLUTION :–

• We know that nth term –

$\\ \implies \large{ \boxed{ \sf {A}_{n} = a + (n - 1)d}}$

• Here –

$\\ \: \: \: { \huge{.}} \: \: \sf {A}_{n} = n \th \: \: term$

$\\ \: \: \: { \huge{.}} \: \: \sf a = first \: \: term$

$\\ \: \: \: { \huge{.}} \: \: \sf d = common \: \: difference$

• First Let's find –

$\\ \implies \sf {A}_{11} = a + (11 - 1)d$

$\\ \implies \sf {A}_{11} = a + 10d$

• And –

$\\ \implies \sf {A}_{12} = a + (12- 1)d$

$\\ \implies \sf {A}_{12} = a + 11d$

• So that –

$\\ \implies \sf {A}_{11} - {A}_{12} = (a + 10d) - (a + 11d)$

$\\ \implies \sf {A}_{11} - {A}_{12} = 10d - 11d$

$\\ \implies \sf {A}_{11} - {A}_{12} = -d$

• Now put the value of 'd' –

$\\ \implies \large { \boxed{ \sf {A}_{11} - {A}_{12} = -3}}$

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• Common difference (d) = 3

${\bf{\blue{\underline{To\:Find:}}}}$

• A11 - A12

${\bf{\blue{\underline{Formula\:Used:}}}}$

$\dagger \: \boxed{\sf{ t_{n} = a + (n - 1)d}}$

${\bf{\blue{\underline{Now}}}}$

$: \implies{\sf{ A_{11} = a + (11 - 1)3}}$

$: \implies{\sf{ A_{11} = a + (10)3}}$

$: \implies{\sf{ A_{11} = a + 30}}$

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$: \implies{\sf{ A_{12} = a + (12 - 1)3}}$

$: \implies{\sf{ A_{12} = a + (11)3}}$

$: \implies{\sf{ A_{12} = a + 33}}$

___________________________________

$\dagger \underline{\frak{ according \: to \: the \: question : }}$

$: \implies{\sf{ A_{11} - A_{12} = (a + 30) - (a + 33) }}$

$: \implies{\sf{ A_{11} - A_{12} = a + 30 - a - 33}}$

$: \implies{\sf{ A_{11} - A_{12} = \cancel {a }+ 30 - \cancel{ a}- 33}}$

$: \implies{\sf{ A_{11} - A_{12} = 30 - 33}}$

$: \implies{\sf{ A_{11} - A_{12} = -3}}$