Question

In the following A.P., find the missing terms:
□, 13, □, 3

Answer 1

Step-by-step explanation:

$\large{\boxed{\sf{\red{hope \: this \: will \: help \: you}}}} >$

plase find the attachment....

Answer 2

$\Large{\underline{\underline{\bf{Given:-}}}}$

$a_2\: = \:13$

$a_4 \: = 3$

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$\Large{\underline{\underline{\bf{To \: Find:-}}}}$

$a_1 \: = ?$

$a_3 \:=?$

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$\Large{\underline{\underline{\bf{Solution:-}}}}$

$⟹a_n = a + (n - 1)d \\ \\⟹a_2 = a + (2 - 1)d \\ \\⟹13 = a + 3d \\ \\⟹ 13 - d = a................(i) \\ \\⟹a_n = a + (n - 1)d \\ \\ ⟹a_4 = a + (4 - 1)d \\ \\⟹ 3 = a + 3d \\ \\ ⟹3 - 3d = a............(ii)$

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${\bold{\underline{\underline{From \:(I) \: and \:(ii):-}}}}$

$⟹13 - d = 3 - 3d \\ \\⟹ 13 - 3 = d - 3d \\ \\ ⟹10 = - 2d \\ \\ ⟹\frac{10}{ - 2} = d \\ \\ ⟹- 5 = d \\ \\ ⟹a_2 + d \: = 13 - 5 \\ \\ ⟹a_3 = 8$

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${\bold{\underline{\underline{Putting\: value \: of \: 'd' \: in \: equation\: (I)}}}}$

$⟹13 - d = a \\ \\⟹ 13 - ( - 5) = a \\ \\ ⟹13 + 5 = a \\ \\⟹ 18 = a$

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${\bold{\underline{\underline{Therefore:-}}}}$

$\boxed{a_1\:=\: 18</p><p>\: \:, \: \:a_3 \: = 8}$

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$\Large{\underline{\underline{\bf{Thanks:-}}}}$