Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.
Given that,
a11 = 38
a16 = 73
We know that,
an = a + (n − 1) d
a11 = a + (11 − 1) d
38 = a + 10d ... (i)
Similarly,
a16 = a + (16 − 1) d
73 = a + 15d ... (ii)
On subtracting (i) from (ii), we get
35 = 5d
d = 7
From equation (i),
38 = a + 10 × (7)
38 − 70 = a
a = −32
a31 = a + (31 − 1) d
= − 32 + 30 (7)
= − 32 + 210
= 178
Hence, 31st term is 178.
