Question

3. The 5th term of an arithmetic sequence is 38 and
the 9th term is 66. What is its 25th term?​

Answer 1

Answer:

a+4d=38........(1)

a+8d=66........(2)

On solving

-4d= -28

d=7

put in.....(1)

a+4d=38

a+4*7=38

a+28=38

a=38-28

a=10

Tn= a+(n-1)d

T25=10+(25-1)7

=10+24*7

=10+189

=199

Answer 2

Answer:

178

Step-by-step explanation:

$a_{n}$ = $a_{1}$ + (n - 1)d

$a_{n}$ is $n^{th}$ term of A.P.

$a_{1}$ is $1^{st}$ term of A.P.

d is a difference

$a_{1}$ + 4d = 38 ... (1)

$a_{1}$ + 8d = 66 ... (2)

(2) - (1)

4d = 28 ⇒ d = 7

$a_{1}$ + 28 = 38 ⇒ $a_{1}$ = 10

$a_{25}$ = 10 + (25 - 1)×7 = 178