Question

Difference between second and first terms of an A.P. = a Difference between third and second terms of the same A.P. = b. Find the value of a in terms of b. folloin​

Answer 1

Answer:

Let the AP series be a,a+d,a+2d,a+3d,...

Given,

a+d-a = a =>> d = a

a+2d-(a+d) =>> d = b

Therefore d = a, d = b =>> a = b = d

ie. a & b equals common difference (d)

Answer 2

Answer:

The formula for finding the nth term in an AP is a(nth term)=a+(n-1)d, where a is the first term and d is the common difference between any two consecutive terms in the sequence.

Now, since the ratio between the 1st and the 2nd term is 2:3, we can write it as -

[a]/[a+(2–1)d]=2/3

[a]/[a+d]=2/3

Further solving this expression -

3[a]=2[a+d]

a=2d.

Now, the ratio between the 3rd to fifth term can be written as -

[a+(3–1)d]/[a+(5–1)d]

=[a+2d]/[a+4d]

We know, from the above expression that a=2d. So substituting a=2d :-

[a+2d]/[a+4d]

=[2d+2d]/[2d+4d]

=4d/6d

=4/6

=2/3

Therefore, the ratio between the 3rd and the 5th terms if the AP is 2:3.