Question

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.​

Answer 1

Answer:

what ??? I dont get u bruhh!!!

Answer 2

Answer:

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

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

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

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

❥ According to given question :

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

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$\Large{\underline{\underline{\bf{Additional Information:-}}}}$

Sum of N Terms of AP And Arithmetic Progression.

❥ Sum of n terms in AP. ↠ n/2[2a + (n – 1)d]

❥ Sum of square of 'n' natural numbers ↠ [n(n+1)(2n+1)]/6

❥ Sum of Cube of 'n' natural numbers ↠ [n(n+1)/2]²

❥ Sum of natural numbers ↠ n(n+1)/2