Question

Find the 31st term of an AP whose 11th term is 38 and 6th term is 73

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The 31st term is -102.

Step-by-step explanation:

Given : An A.P whose 11th term is 38 and 6th term is 73.

To find : The 31st term of an A.P?

Solution :

The nth term of an A.P is $a_n=a+(n-1)d$

We have given,

11th term is 38.

i.e. $a_{11}=a+(11-1)d$

$38=a+10d$ ......(1)

6th term is 73.

i.e. $a_{6}=a+(6-1)d$

$73=a+5d$ .....(2)

Solving equation (1) and (2) by subtracting them,

$a+10d-a-5d=38-73$

$5d=-35$

$d=-\frac{35}{5}$

$d=-7$

Substitute in equation (1),

$a+10(-7)=38$

$a-70=38$

$a=38+70$

$a=108$

Now, The 31st term is $a_{31}=a+(31-1)d$

$a_{31}=a+(30)d$

Substitute a and d,

$a_{31}=108+(30)(-7)$

$a_{31}=108-210$

$a_{31}=-102$

Therefore, The 31st term is -102.