Question

2) If each term of A.Pis doubled the resulting sequence also in A.P write its first term and
common difference and nth term.​

Answer 1

2a

2a+2d

2a+4d

first term=a

common difference=2a+2d-2a

=2d

nth term = 2a+(n-1)2d

take out 2 as common

so that would be 2{a+(n-1)d}

Answer 2

The first terms, common difference, nth term are shown below.

Let us examine the two cases by taking examples.

Let for the first case, AP be = 1, 3, 5, 7, 9...

Here, first term (a) = 1.

Common difference between two terms  (d) = 3 - 1 = 2.

nth term in the AP is given is as:

an = a + (n-1)d

= 1 + (n-1)(2)

= 1 + 2n - 2

= 2n -1

When each term of the AP is doubled, we get the AP as: 2, 6, 10, 14, 18, ...

Here, first term is (a') = 2.     [Twice that of a]

Common difference is given as (d') = 6 - 2 = 4.     [Twice that of a]

nth term in AP is given as:

an = a' + (n-1)d'

= 2 + (n-1)4

= 2 + 4n - 4

= 4n - 2  , which is twice the previous expression.