Question

What is nth term of ap​ a,a+2d,a+3d.....

Answer 1

The nth term of the A.P. a, a + d, a + 2d, a + 3d, ... is a + (n - 1) d.

Step-by-step explanation:

The first term of the given A.P. is $a$ and the common difference is $d$.

Let the terms of the given A.P. be given by $t_{1},t_{2},t_{3},t_{4},...,t_{n},...$. Then

• $t_{1}=a=a+(1-1)d$

• $t_{2}=a+d=a+(2-1)d$

• $t_{3}=a+2d=a+(3-1)d$

• $t_{4}=a+3d=a+(4-1)d$

Continuing this way, we can obtain the nth term of the A.P.,

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

Extra:

For the given A.P., the sum of first n terms

$\quad S_{n}=t_{1}+t_{2}+t_{3}+...+t_{n}$

$\Rightarrow S_{n}=a+(a+d)+...+(a+\overline{n-1}d)$

$\Rightarrow \boxed{S_{n}=\dfrac{n}{2}[2a+(n-1)d]}$