Question

If the first term of first Ap1 is -7 and the first term of second Ap2 is 11 and the common difference of both the Ap's is same, then the difference between their 127th terms can be​:
1: 128
2: 36
3: 18
4: 4

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let first term of AP is a1 and of second AP is a2, and common difference of both AP is d.

Than,

→ 127th term of first AP = a1 + (n - 1)d

→ T(127) = a1 + (127 - 1)d

→ T(127) = a1 + 126d

Putting given value of a1 = (-7) Now,

→ T(127) = (-7) + 126d ------- Eqn.(1) .

Similarly,

→ 127th term of second AP = a2 + (n - 1)d

→ T(127) = a2 + (127 - 1)d

→ T(127) = a2 + 126d

Putting given value of a1 = 11 Now,

→ T(127) = 11 + 126d ------- Eqn.(2) .

Now, we have to find , the difference between their 127th terms..

So ,

→ Eqn.(1) - Eqn.(2)

→ {(-7) + 126d} - {11 + 126d}

→ (-7) - 11 + 126d - 126d

→ (-18)

And,

→ Eqn.(2) - Eqn.(1)

→ {11 + 126d} - {(-7) + 126d}

→ 11 - (-7) + 126d - 126d

→ 11 + 7

→ 18.

Hence, Option (3) , 18 is correct Answer.