Question

Determine the A.P whose 3rd term is 5 and the 7th term is 9​

Answer 1

a+2d = 5

a + 6d = 9

-4r = -4

r = 4

a+8 = 5

a = -3

AP: -3,1,5,9.......

Answer 2

Answer:

$\huge{\pink{\boxed{\green{\sf{A.P=3,4,5,6,7........}}}}}$

Step-by-step explanation:

$\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

$\: {\orange{given}} \\ { \pink{ \boxed{ \green{a3 = 5}}}} \\ { \pink{ \boxed{ \green{a7 = 9}}}} \\ \\ { \blue{to \: find}}\\ { \purple{ \boxed{ \red{ap = }}}}$

☆ According to given question:

$\to a3 = 5 \\ \to a + 2d = 5 - - - - - (1) \\ \to a7 = 9 \\ \to a + 6d = 9 - - - - - (2)\\ \\ subtracting \: (1) \: from \: (2) \\ \to a + 6d - (a + 2d) = 9 - 5 \\ \to a + 6d - a - 2d = 4 \\ \to 4d = 4 \\ \to d = 1 \\ \\ putting \: value \: of \: d \: in(1) \\ \to a + 2d = 5 \\ \to a + 2 \times 1 = 5 \\ \to \: a = 5 - 2 \\ \to a = 3 \\ \\ \to hence \: the \: required \\{ \pink{ \boxed{ \green{ \therefore A.P = 3,4,5,6,7.......}}}}$

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