Question

two aps have the same common difference the first term of one ap is -1 and that of the other is -8 then the difference between their 4th terms is

Answer 1

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7

EXPLANATION:-

LET THE SAME COMMON DIFF. OF A.P. BE d

$first \: term \: of \: 1st \: a.p. = - 1$

$forth \: term \: of \: 1st \: ap = ( - 1 + 3d)$

$f1st \: term \: of \: 2nd \: a.p. \: = - 8$

$forth \: term \: of \: 2nd \: a.p. = ( - 8 + 3d)$

$then \: (a_{ 4)_{1st \: ap}} - (a_{ 4)_{2nd \: ap}} = (- 1 + 3d)( - 8 + 3d)$

$= - 1 + 3d + 8 - 3d = 7$

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Answer 2

Answer:

7 or -7

Step-by-step explanation:

Let the two airthematic progression names AP1 and AP2

Given:

First term of AP1 = a1 = -1

First term of AP2 = a2 = -8

Let the common difference of AP1 and AP2 be d and d1 respectively

But according to question,

d = d1

Now, Fourth term of AP1 = a1 + 3d = -1 + 3d

Fourth term of AP2 = a2 + 3(d1) = -8 + 3(d1) = -8 + 3d     {as d1 = d}

Now, difference between their 4th terms (AP1 -AP2)  = (-1 + 3d) - (-8 + 3d)

= -1 + 3d + 8 - 3d = 7

But there is another possibility also,

Here i have taken out AP1 - AP2

But, we need to calculate AP2 - AP1 also

As in question it is asked to find difference but it is not specified its order that is AP1 - AP2 or AP2 - AP1

So, difference between their 4th terms (AP2 - AP1) = (-8 + 3d) - (-1 + 3d)

= -8 + 3d +1 - 3d = -7

Therefore, Difference = -7 or 7

Hope, you got it :-))

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