Question

find the 31st term of an ap whose 11th term is 38 and the 16th term is 73 ​

Answer 1

Given:

$\tt{a_{11} = 38}$

$\tt{a_{16} = 73}$

To find:

$\tt{a_{31}}$

Solution:

a + 10d = 38

=> a = 38 - 10d ..(1)

a + 15d = 73

Put (1):

=> 38 - 10d = 73 - 15d

=> 5d = 35

=> d = 7

a + 30d = 38 - 10d + 30d

=> 38 + 20d

=> 38 + 20(7)

=> 38 + 140

=> 178

Formula used:

$\tt{a_{n} = a + (n - 1)d}$

___________

Answer 2

Answer: 178

Step by step explanation:

Given:

a11 = 38 and a16 = 73

To find: a31 ( 31st term)

Solution:

a + 10d = 38

=> a = 38 - 10d ___(1)

a + 15d = 73

Putting (1):

=> 38 - 10d = 73 - 15d

=> 5d = 35

=> d = 7

.°. a + 30d = 38 - 10d + 30d

=> 38 + 20d

=> 38 + 20×(7)

=> 38 + 140

=> 178

Thus, The 31st term is 178.