Question

Find the 20 th term of an arithmetic sequence if its 6 th term is l4 and 14 th term is 6.​

Answer 1

Let a and d are first term and Common \: difference \: of \: an \: A .P Common difference of an A.P

/* We know that */

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

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

a 6 =14

⟹a+5d=14−−(1)

and \: a_{14} = 6and a =6

⟹a+13d=6−−(2)

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

8d = -8d=−8

$\implies d = \frac{-8}{8}⟹d= -8$

⟹d=−1−−(3)

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

a + 5 \times (-1) = 6a+5×(−1)=6

⟹a−5=6

⟹a=6+5

⟹a=11−−(4)

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

=a+19d

=11+19(−1)

=11−19

= -8

Therefore.,

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

$\green { = -8 }$