Question

Find the 20th term of an arithmetic sequence, if its 6th term is 14 and 14th terms is 6
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Answer 1

Answer:

the 20th term is 0.......

Answer 2

$Let \: 'a' \:and \: 'd' \: are \: first \:term \:and$

$Common \: difference \: of \: an \: A .P$

/* We know that */

$\boxed{\pink{ n^{th} \:term (a_{n}) = a+(n-1)d}}$

$Here , given \: a_{6} = 14$

$\implies a + 5d = 14 \: --(1)$

$and \: a_{14} = 6$

$\implies a + 13d = 6 \: --(2)$

/* Subtract equation (1) from equation (2), we get */

$8d = -8$

$\implies d = \frac{-8}{8}$

$\implies d = -1 \: --(3)$

/* Put d = -1 in equation (1) , we get */

$a + 5 \times (-1) = 6$

$\implies a - 5 = 6$

$\implies a = 6 + 5$

$\implies a = 11\: --(4)$

$Now, \red{ 20^{th} \:term \:( a_{20}) }$

$= a + 19d$

$= 11 + 19(-1)$

$= 11 - 19$

$= -8$

Therefore.,

$\red{ 20^{th} \:term \:( a_{20})\: of \: A.P }$

$\green { = -8 }$

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