Question

if for an A.P.,d= -4, then t20-t15=?

Answer 1

Answer:

The answer is -20

Step-by-step explanation:

Concept:

General term of an A.P. with first term $a$ and common difference $d$ is

                             $\boxed{t_n=a+(n-1)d}$

     $\Rightarrow t_{20}=a+(20-1)d=a+19d=a+19(-4)=a-76$

And $t_{15}=a+(15-1)d=a+14d=a+14(-4)=a-56$

Therefore

     $t_{20}-t_{15}=a-76-(a-56)=a-76-a+56=-20$

Answer 2

EXPLANATION.

If for an A.P.

Common difference = d = - 4.

As we know that,

Formula of :

General term of an A.P.

⇒ Tₙ = a + (n - 1)d.

Using this formula in the equation, we get.

To find : T₂₀ - T₁₅.

⇒ T₂₀ = a + (20 - 1)d.

⇒ T₂₀ = a + 19d.

⇒ T₁₅ = a + (15 - 1)d.

⇒ T₁₅ = a + 14d.

⇒ (a + 19d) - (a + 14d).

⇒ a + 19d - a - 14d.

⇒ 19d - 14d.

⇒ 5d = 5 x (- 4) = - 20.

⇒ T₂₀ - T₁₅ = - 20.

                                                                                                                 

MORE INFORMATION.

Supposition of terms in an A.P.

(1) Three terms as : a - d, a, a + d.

(2) Four terms as : a - 3d, a - d, a + d, a + 3d.

(3) Five terms as : a - 2d, a - d, a, a + d, a + 2d.