Question

 Find the last term of the AP 25,22,19.........? whose sum is 101​

Answer 1

Answer:

we have,

A.P. is

25,22,19......

S  

n

​  

=116

a=25

d=T  

2

​  

−T  

1

​  

 

d=22−25

d=−3

Then, we know that

S  

n

​  

=  

2

n

​  

(2a+(n−1)d)

⇒116=  

2

n

​  

(2×25+(n−1)×(−3))

⇒116=  

2

n

​  

(50−3n+3)

⇒116=  

2

n

​  

(53−3n)

⇒232=n(53−3n)

⇒3n  

2

−53n+232=0

⇒3n  

2

−(29+24)n+232=0

⇒3n  

2

−29n−24n+232=0

⇒n(3n−29)−8(3n−29)=0

⇒(3n−29)(n−8)=0

If

3n−8=0

n=  

3

8

​  

(notpossible)

If

n−8=0

n=8

So,

The last term is

S  

n

​  

=  

2

n

​  

(a+l)

116=  

2

8

​  

(25+l)

116=4(25+l)

116=100+4l

116−100=4l

4l=16

l=4

Hence, the last term of this series is

4.

This is the answer.

Step-by-step explanation:Easy Explained please mark me as Brainlist