Question

the 2nd and 8th term of an arithmetic progression are 17 and 1 respectively. What is the 14th term ?

Answer 1

$\mathfrak {\huge {Hi !}}$

$\tt{a_{2} = 17}$

$\tt {a_{8} = 1}$


a + (2 - 1)d = 17

=》 a + d = 17

=》 a = 17 - d ... (1)


a + (8 - 1)d = 1

=》 a + 7d = 1

=》 a = 1 - 7d ... (2)


(1) = (2)


=》 17 - d = 1 - 7d

=》 $\tt {d = \frac {(-8)}{3}}$


=》 $\tt {a = \frac {59}{3}}$


14th term = a + (14 - 1)d

=》a + 13d

=》 $\huge {\sf {(-15)}}$