Question

Find the ap whose third term is 5 and seventh termis9

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{A.P=-3,-1,1,3,...}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Third \: term = 5 \\ \\ \tt: \implies Seventh\: term = 9 \\ \\ \red{\underline \bold{To \:Find :}} \\ \tt: \implies A.P = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies a_{5} = 5 \\ \\ \tt: \implies a + 4d = 5 - - - - - (1) \\ \\ \bold{Similarly : } \\ \tt: \implies a_{7} = 9 \\ \\ \tt: \implies a + 6d = 9 - - - - - (2) \\ \\ \text{Subtracting \: (1) \: from \: (2)} \\ \tt: \implies a + 6d - (a + 4d) = 9 - 5 \\ \\ \tt: \implies a + 6d - a - 4d = 4 \\ \\ \tt: \implies 2d = 4 \\ \\ \green{\tt: \implies d = 2} \\ \\ \text{Putting \: value \: of \: d \: in \: (1)} \\ \tt: \implies a + 4 \times 2 = 5 \\ \\ \tt: \implies a + 8 = 5 \\ \\ \tt: \implies a = 5 - 8 \\ \\ \green{\tt: \implies a = - 3} \\ \\ \green{\tt \therefore A.P= - 3, - 1,1,3,...}$

Answer 2

Answer:

➡️Given:

⟹Thirdterm=5

⟹Seventhterm=9

ToFind:

⟹A.P=?

• According to given question :

As we know that

⟹a5 =5

⟹a+4d=5−−−−−(1)

Similarly:

⟹a7 =9

⟹a+6d=9−−−−−(2)

Subtracting (1) from (2) , we get ,

⟹a+6d−(a+4d)=9−5

⟹a+6d−a−4d=4

⟹2d=4

⟹d=2

Putting value of d in (1)

⟹a+4×2=5

⟹a+8=5

⟹a=5−8

⟹a=−3

∴A.P=−3,−1,1,3,........