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