Question

Two aps have the same common difference the first term of one of these is -1 and that of the other is -8 then the difference between their 4th term is?​

Answer 1

Answer:

The difference between their 4th term is 7.

Step-by-step explanation:

Given :-

• Two APs have the same common difference.
• The first term of one of these is -1 and the other is -8.

To find :-

• Difference between their 4th term.

Solution :-

Formula used :

${\boxed{\sf{T_n=a+(n-1)d}}}$

• a = first term
• d = Common difference

Common difference of 1st AP = Common difference of 2nd AP = d

Now find the 4th term of 1st and 2nd AP.

★ In case of 1st AP,

• a = -1
• n = 4
• common difference = d

$\to\sf{T_4=-1+(4-1)d}$

$\to\sf{T_4=-1+3d}$

$\to\sf{T_4=3d-1}$

★In case of 2nd AP,

• a = -8
• n = 4
• common difference = d

$\to\sf{t_4=-8+(4-1)d}$

$\to\sf{t_4=-8+3d}$

$\to\sf{t_4=3d-8}$

Difference between their 4th term,

$\sf{=T_4-t_4}$

= 3d-1-(3d-8)

= 3d-1-3d+8

= 7

Therefore, the difference between their 4th term is 7.