Question

for the A.P. -3,-7,-11......, can we find A 30-A 20 without actually finding A 30 and A20 ? give reasons for your ans ?

Answer 1

Answer,

It's True!!

First term, a = - 3

Common difference, d = a2 - a1 = - 7 - (- 3) = - 4

a30 - a20 = a + 29d - (a + 19d)

= 10d

= - 40

It is so because difference between any two terms of an AP is proportional to common difference of that AP !!

Thanks!!

Answer 2

∵ nth term of an AP, an = a + (n-1)d

∴ a30 = a + (30 - 1)d = a + 29d ...1)

and a20 = a + (20 - 1)d = a + 19d ....2)

Now, a30 - a20 = (a + 29d) - (a+19d) = 10d

and from given AP common difference, d = a2-a1 = -7-(-3) = -7+3 = -4

∴ a30 - a20 = 10(-4) = - 40