It is given that,

• (a) First term of the AP is 15.
• (l) Last term of the AP is -42.
• (d) Common difference is -3.

We have to find the number of terms and the sum of the numbers in the AP.

We know that,

aₙ = a + (n − 1) × d

Putting the values, we get :

=》- 42 = 15 + (n - 1) -3

=》- 42 - 15 = (n - 1) - 3

=》- 57 = (n - 1) - 3

=》57 = (n - 1) 3

=》57 / 3 = (n - 1)

=》19 = (n - 1)

=》n = 20.

Hence,

The number of terms in the AP are 20.

Now, Calculating Sum :

We know that,

Sₙ = n/2 [2a + (n − 1) × d]

Putting the values, we get :

=》Sₙ = 20/2 [2( 15 ) + 19( -3 )]

=》Sₙ = 10 [30 - 57]

=》Sₙ = 10 ( - 27 )

=》Sₙ = - 270.

Hence,

The sum of numbers in the AP is - 270.