Question

how to find the general term of an AP with derivation and examples

Answer 1

Answer:

Step-by-step explanation:

Arithmetic Progression ( A.P ).

Arithmetic Progression  is a sequence of numbers such that the difference between any two consecutive terms is constant and  the  constant value is called the common difference( d ).

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

Let

d = common difference

a1 = a = first term

a2 = second term

a3 = third term   and so on.

am = mth term

an = nth term (last term  ).

 d = a2 − a1 = a3 − a2  and so on.

 a1 = a1

a2 = a1 + d

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

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

an = a + ( n − 1 ) d

So  the general term of an AP  is an = a + ( n−1 ) d

Answer 2

Answer

the general term is an and its formula is a+(n-1)d

Step-by-step explanation:

example: you are given that a= 2 , d=5 and n= 10

then an= a+(n-1)d

            = 2+(10-1)5

            = 2+9*5

            = 2+45

            = 47, where a is first term, d is common difference and n is the total number of terms in the AP.

therefore the general term in this example is 47.