Question

the 5th term of an ap is 1 and 31st term is minus 77 find the 11th term​

Answer 1

please see the attached photo for your answer

Answer 2

Answer:

Required value of 11th term is - 17.

Step-by-step explanation:

Given, 5th term of an AP is 1 and 31st term is - 77.

Let the first term of the AP be a and common difference between the terms be d.

From the properties of AP : -

• nth term = a + ( n - 1 )d, where a is the first term, d is the common difference between the terms and n is the number of terms.

According to the question : -

= > 5th term = 1

= > a + ( 5 - 1 )d = 1

= > a + 4d = 1

= > a = 1 - 4d                       ...( i )

= > 31st term = - 77

= > a + ( 31 - 1 )d = - 77

= > a + 30d = - 77

= > a = - 77 - 30d             ...( ii )

Comparing the values of a from ( i ) and ( ii ) : -  

= > 1 - 4d = - 77 - 30d

= > 30d - 4d = - 77 - 1

= > 26d = - 78

= > d = - 78 / 26

= > d = - 3

Substituting the value of d in ( i ) : -

= > a = 1 - 4d

= > a = 1 - 4( - 3 )

= > a = 1 + 12

= > a = 13

Hence the required value of a is 13 and d is - 3.

Therefore,

= > 11th term = a + ( 11 - 1 )d

= > 11th term = 13 + 10( - 3 )

= > 11th term = 13 - 30

= > 11th term = - 17

Hence the required value of 11th term is - 17.