Question

in an arithmetic sequence, the 5th term is 27 while the 10th term is 52. What is the 25th term?

Answer 1

Answer:

$\huge{\boxed{\rm{\pink{a25=127}}}}$

Step-by-step explanation:

Given:-

In an arithmetic sequence, the 5th term is 27 while the 10th term is 52.

To find:-

What is the 25th term?

Solution:-

we know that the general term of an AP is

an=a+(n-1)d

now,5th term =27

=>a5=a+4d=27----(1)

10th term =52

=>a10=a+9d=52-----(2)

Now solving (1)&(2)

a+4d=27

a+9d=52

(-)

------------

0-5d=-25

------------

=>-5d=-25

=>5d=25

=>d=25/5

=>d=5

Common difference=5

and from (1)

=>a+4(5)=27

=>a+20=27

=>a=27-20

=>a=7

First term=7

25th term=a25

=>a+24d

=>7+24×5

=>7+120

=>127

Answer:-

25th term of the AP=127