Question

Two AP’s 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
A. -1
B. -8
C. 7
D. -9

Answer 1

Hint: In this particular type of question we have to assume two AP's with the first term -1 and -8 respectively and an equal common difference . Then we have to proceed by finding the fourth term of both the AP's using the formula of nth term of an AP . At last we have to subtract and cancel out the common difference ( d ) to get the required answer.

Complete step-by-step answer:
Let the first AP = ${a_1},{a_2},{a_3} \ldots \ldots {a_n}$
And the second AP = ${b_1},{b_2},{b_3} \ldots \ldots \ldots {b_n}$

Let the common difference of both be (d) as the common difference of both AP’s are equal .
Also , ${a_1} = - 1$
${b_1} = - 8$
Since , ${a_n} = a + \left( {n - 1} \right)d$
$
  {a_4} = - 1 + \left( {4 - 1} \right)d \\
   \Rightarrow {a_4} = - 1 + 3d \\
$
Similarly ,
$
  {b_4} = - 8 + \left( {4 - 1} \right)d \\
   \Rightarrow {b_4} = - 8 + 3d \\
$
Now, the difference between both terms,
$
  {a_4} - {b_4} = \left( { - 1 + 3d} \right) - \left( { - 8 + 3d} \right) \\
   \Rightarrow {a_4} - {b_4} = 7 \\
$

Note: Remember to recall the basic formula of the nth term of an AP to solve these types of questions. Note that it is important that the unknown value (d) gets cancelled out to get the difference between the two terms in such types of questions. Also keep in mind that to find the difference we can subtract either one of the AP's from the other and check for the answer in the options given.