Question

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

Answer 1

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 created by pragatimaniyar13

Answer 2

$\begin{gathered} \\ \Large{\bf{\green{\underline{AnSwEr\::}}}} \\ \end{gathered}$

25th term of an arthematic sequence = 185

$\begin{gathered} \\ \Large{\bf{\red{\underline{GiVeN\::}}}} \\ \end{gathered}$

• 5th term of an arthematic sequence = 38
• 9th term of an arthematic sequence = 66

$\begin{gathered} \\ \Large{\bf{\purple{\underline{To \: FiNd\::}}}} \\ \end{gathered}$

• 25th term of arthematic sequence

$\begin{gathered} \\ \Large{\bf{\pink{\underline{SoLuTiOn\::}}}} \\ \end{gathered}$

5th term of an arthematic sequence = 38

⇒a + 4d = 38---------------------------(1)

9th term of arthematic sequence = 66

⇒a + 8d = 66---------------------------(2)

( a + 8d ) - ( a + 4d ) = 66 - 38

⇒ a + 8d - a - 4d = 28

⇒4d = 28

⇒d = 28 ÷ 4

⇒d = 7

Put the value of d in equation (1) we get,

⇒a + 4( 7 ) = 38

⇒a + 28 = 38

⇒a = 38 - 28

⇒a = 10

25th term of an arthematic equation

⇒a + 25d

⇒10 + 25( 7 )

⇒10 + 175

⇒185

25th term of an arthematic sequence = 185