Question

Find the $31^{st}$ term of an AP whose $11^{th}$ term is 38 and the $16^{th}$ term is 73.

Answer 1

Given that, $a_{11} = 38$ and $a_{16} = 73$
We know that,
$a_n = a + (n − 1) d$
$a_{11} = a + (11 − 1) d$
$38 = a + 10d$ ……..(1)
Similarly,
$a_{16} = a + (16 − 1) d$
$73 = a + 15d$ …….(2)
On subtracting (1) from (2), we obtain
$35 = 5d$
$d = 7$
From equation (1),
$38 = a + 10 × (7)$
$38 − 70 = a$
$a = −32$
$a_{31} = a + (31 − 1) d$
$a_{31}= − 32 + 30 (7)$
$a_{31}= − 32 + 210$
$a_{31}= 178$

Hence, $31^{st}$ term is $178$.