Question

The 24th term of an AP is twice its 10th term. Show that its 72nd term is 4 times its 15th term.


Class 10

Arithmetic Progressions

Answer 1

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here's the solution...

Answer 2

24 th term of AP.

A 24 = a + ( 24 - 1 ) d

❇ A 24 = a + 23 d

10 th term of the A. P.

A 10 = a + ( 10 - 1 ) d

❇ A 10 = a + 9 d

ACCORDING TO THE QUESTION,

A 24 = 2 * A. 10

a + 23 d = 2 * ( a + 9 d )

a + 23 d = 2a + 18 d

2a - a = 23 d - 18 d

a = 5 d ----> ( i )

72 th term of the A. P.,

A 72 = a + ( 72 - 1 ) d

❇ A72 = a + 71 d

A 72 = 5d + 71 d

❇ A 72 = 76 d

A 15 = a + ( 15 - 1 ) d

A 15 = a + 14d

A. 15 = 5d + 14 d

❇ A 15 = 19 d

We need to prove..

A 72 = 4 ( A 15 ).

PROOF :

A 72 / A 15 = 4

76 d / 19 d = 4

4 = 4

⏺️L. H. S = R. H. S.

✔️PROVED.