Question

In an AP the 24th term is twice the 10th term prove that 72 term is twice the 34th term​

Answer 1

now mate

nth term formula is

a+(n-1)d

where a is first term

n is number of terms

d is common difference

a+(24-1)d=2(a+(10-1)d)

a+23d=2a+18d

a=(23-18)d

a=5d

now

a+(72-1)d

5d+71d

76d

now

76d=10d+66d

=2a+2(34-1)d

2(a+(34-1)d)

so it is 34th tetm

Answer 2

Solution:-

Given:-

• 24th term is twice the 10th term.

To Prove:-

• 72th term is twice the 34th term.

Proof:-

24th term is twice the 10th term.

=) a24 = 2 × a10

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

=) a + 23d = 2a + 18d

=) 2a - a = 23d - 18d

=) a = 5d ___________(1)

Now,

We need to prove that, 72th term is twice the 34th term.

=) a72 = 2 ( a34)

L.H.S. a72

=) a72 = a + 71d

=) a72 = 5d + 71d [ from eq(1) ]

=) a72 = 76d

R.H.S. 2( a34)

=) 2( a34) = 2 ( a + 33d )

=) 2 ( a34) = 2a + 66d

=) 2( a34) = 2(5d) + 66d [ from eq(1) ]

=) 2(a34) = 10d + 66d

=) 2(a34) = 76d

L.H.S. = R.H.S

Hence Proved!