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 terms is

Answer 1

Answer:

Let the common difference of both the A.P's be 'd'.

Given the first terms are -1 and -8.

As we know an A.P is in the form,

Tn = a +(n-1)d.

Let the Two A.P's be An and Tn.

Now according to the question,

A4 = -1 + (4-1)d

= -1 + 3d

T4 = -8 +(4-1)d

= -8 + 3d

Difference between the two terms is;

A4 - T4 = (-1 +3d) - (-8+3d)

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

= 7

Answer 2

☛ Question :-

Two APs have the same common difference. The first term of one of these is -1 and that of the other is -8. The difference between their 4th terms is

☛ To find :-

• The difference between their 4th term

☛ Formula to be used :-

• an = a + (n - 1) d

☛ Solution :-

Let us Assume,

AP ① :- a1, a2, a3, a4,....

AP ② :- b1, b2, b3, b4,.....

• Common difference of AP ① = d1
• Common difference of AP ② = d2

a1 = -1, b1 = -8, d1= d2 = d (say)

using formula,

an = a + (n - 1) d

• a = first term
• d = common difference

a4 = -1 + (4 - 1) d

= -1 + 3d ________( 1 )

b4 = -8 + (4 - 1) d

= -8 + 3d ________( 2 )

a4 - b4 = (-1 + 3d) - (-8 + 3d)

= -1 + 3d + 8 - 3d

= 7

☛ Difference between their 4th terms = 7