Determine the A.P whose 3rd term is 5 and the 7th term is 9
Question
2 Answer

1. User Answers neelrambhia03
a+2d = 5
a + 6d = 9
4r = 4
r = 4
a+8 = 5
a = 3
AP: 3,1,5,9.......

2. User Answers BrainlyConqueror0901
Answer:
[tex]\huge{\pink{\boxed{\green{\sf{A.P=3,4,5,6,7........}}}}}[/tex]
Stepbystep explanation:
[tex]\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION}}}}}}}[/tex]
[tex] \: {\orange{given}} \\ { \pink{ \boxed{ \green{a3 = 5}}}} \\ { \pink{ \boxed{ \green{a7 = 9}}}} \\ \\ { \blue{to \: find}}\\ { \purple{ \boxed{ \red{ap = }}}}[/tex]
☆ According to given question:
[tex] \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.......}}}}[/tex]
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