Question

Find, 100 is a term of the A.P.25,28,31,......... or not

Answer 1

hello users .....

Given AP is :
25,28,31,.......

we have to find :
nth term (An) = 100 or not .

Solution :-
Here,
a ( first term) = 25
d ( common difference ) = a2 ( second term ) - a (first term)

=> d = 28 - 25 = 3

n = ? 

And 
An = 100

We know that:
An = a + (n-1)d 

=> 100 = 25 + ( n - 1) × 3 

=> 100 = 25 + 3n - 3 

=> 100 - 25 + 3 = 3n 

=> 78 = 3n 

=> n = 26 

Hence;
100 is 26th term of  Ap : 25,28,31,.. 

# hope it helps :)

Answer 2

Answer:

100 is the 26th term.

Step-by-step explanation:

An arithmetic progression or arithmetic sequence exists as a sequence of numbers such that the difference between the consecutive terms exists constant.

Given,

A.P.25,28,31,.........

To find,

100 is a term of the A.P or not.

Step 1

$&25+28+31+\ldots \ldots+100$

a ( first term) = 25

d ( common difference ) = a2 ( second term ) - a (first term)

$\Rightarrow d=28-25=3$

Here,

Let the number of terms be "n ",

$25+(n-1) \times 3 &=100$

$&(n-1) \times 3 &=75$

$& & n &=26$

Hence, 100 is the 26th term of the given A.P.

#SPJ3