Question

plzzz solve the question exparts

Answer 1

A refer to first term

N refers to position of term that want

D is common difference

Tn = term u want

Example :

1,2,3,4,5,6

Here a=1

D= 2-1
=1

If u want 4th term then:

N=4

Tn=4

Therfore

4 = 1 + (4-1)1

4=1+3

4=4

{---->Or<----}

Arithmetic Progression, AP
Definition

Arithmetic Progression (also called arithmetic sequence), is a sequence of numbers such that the difference between any two consecutive terms is constant. Each term therefore in an arithmetic progression will increase or decrease at a constant value called the common difference, d.

Examples of arithmetic progression are:

2, 5, 8, 11,... common difference = 3

23, 19, 15, 11,... common difference = -4

Derivation of Formulas
Let
dd = common difference
a1a1 = first term
a2a2 = second term
a3a3 = third term
amam = mth term or any term before anan
anan = nth term or last term

d=a2−a1=a3−a2=a4−a3d=a2−a1=a3−a2=a4−a3 and so on.

Derivation for an in terms of a1 and d
a1=a1a1=a1

a2=a1+da2=a1+d

a3=a2+d=(a1+d)+d=a1+2da3=a2+d=(a1+d)+d=a1+2d

a4=a3+d=(a1+2d)+d=a1+3da4=a3+d=(a1+2d)+d=a1+3d

a5=a4+d=(a1+3d)+d=a1+4da5=a4+d=(a1+3d)+d=a1+4d
...

am=a1+(m−1)dam=a1+(m−1)d
...

an=a1+(n−1)d