Question

write first term,and second term. 2:3​

Answer 1

Answer:

First term=2

Second term =3

Answer 2

Step-by-step explanation:

the formula for finding the nth term is 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 term in the sequence.

Now, since the ratio between the 1 st and the 2 nd 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

=2/3

therefore, the the ratio between the 3rd term and the 5 th terms ,AP is 2:3.