Math, asked by dashmesh6096, 11 months ago

The 16th term of an ap is 1 more than twice its 8th term . If the 12th term of the ap is 47 ,then find its nth term

Answers

Answered by BrainlyConqueror0901
24

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

\green{\tt{\therefore{nth\:term\:of\:A.P=4.8n-10.6}}}

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

 \green{\underline \bold{Given:}} \\  \tt:  \implies  a_{16} = 1 + 2 a_{8} \\  \\  \tt:  \implies 12th \: term \: of \: A.P = 47 \\  \\   \red{\underline \bold{To \: Find:}}\\  \tt:  \implies nth \: term \: of \: A.P = ?

• According to given question :

 \bold{As \: we \: know \: that} \\  \tt:  \implies  a_{16} = 1 + 2 a_{8} \\  \\  \tt:  \implies a + 15d = 1 + 2(a + 8d) \\  \\ \tt:  \implies a + 15d = 1 + 2a + 16d \\  \\ \tt:  \implies a + d =  - 1 -  -  -  -  - (1) \\  \\  \bold{For \: a _{12} : }  \\   \tt:  \implies  a_{12} = 47 \\  \\  \tt:  \implies a + 11d = 47 -  -  -  -  - (2) \\  \\ \text{Subtracting \: (1) \: from \: 2} \\  \tt:   \implies 11d - d = 47 - ( - 1) \\  \\ \tt:  \implies 10d = 48 \\  \\  \green{\tt:  \implies d = 4.8} \\  \\  \text{Putting \: value \: of \: d \: in \: (1)} \\  \tt:  \implies a + 4.8 =  - 1 \\  \\ \tt:  \implies a =  - 1 - 4.8 \\  \\  \green{\tt:  \implies a =  - 5.8} \\  \\  \bold{As \: we \: know \: that} \\  \tt:  \implies  a_{n} = a + (n - 1)d \\  \\ \tt:  \implies  a_{n} = - 5.8 +( n - 1) \times 4.8 \\  \\ \tt:  \implies  a_{n} =  - 5.8 + 4.8n - 4.8 \\  \\  \green{\tt:  \implies  a_{n} =4.8n - 10.6}

Answered by Saby123
32

</p><p>\tt{\pink{Hello!!! }}

</p><p>\tt{\red{Given \: - }}

We Know That :

According to the Question ;

 \tt{ \purple{a \:  +  \: 15d \:  = 2a \:  +  \: 14d + 1 \: }}.......(1)

 \tt{ \orange{a \:  +  \: 11d \:  =  \: 47 \: }}........(2)

Solving We Get :

</p><p>\tt{\red{d = 4.8 }} \\ \\  \tt{\blue{a = -5.8 }}

We Know That :

</p><p>\tt{\green{\implies{a_{n} = a + (n-1)d = 4.8 n - 10.6}}}.......(A)

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