Question -
Answer -
Given:
24th termis twice the 10th term
So, a24 =2a10
We need to prove: a72 =2a34
We know, an =a + (n – 1) d [where a is first term or a1 and d is common differenceand n is any natural number]
When n = 10:
a10 =a + (10 – 1)d
= a + 9d
When n = 24:
a24 =a + (24 – 1)d
= a + 23d
When n = 34:
a34 =a + (34 – 1)d
= a + 33d ………(i)
When n = 72:
a72 =a + (72 – 1)d
= a + 71d
According to question:
a24 =2a10
a + 23d = 2(a + 9d)
a + 23d = 2a + 18d
a – 2a + 23d – 18d = 0
-a + 5d = 0
a = 5d
Now, a72 =a + 71d
a72 =5d + 71d
= 76d
= 10d + 66d
= 2(5d + 33d)
= 2(a + 33d)[since, a = 5d]
a72 =2a34 (From (i))
Hence Proved.