Question

In a certam A.P the 24th term is twice the 10th term prove that the 72nd term is twice the 34th
term​

Answer 1

♡ Heya user ♡

☯Given:-

⇒24th term is twice the 10th term.

☯ To Prove :-

⇒ The 72nd term is twice the 34th term.

Or, a( 72) = 2 a (34)

☯ Solution :

▪ Let us take the first term of the A.P as a

&

▪ Common difference as d.

Hence, let us first find the two terms.

As we know that....

a(n) = a + (n-1)d

✡ So, the 10th term __

n=10

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

= a +9d

✡ 24th term ___

n=24

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

= a+23d

Hence, given that ___

a(24) = 2a(10)

Now, we get

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

⟹ 23d - 18d = 2a -a

⟹ 5d =a ___________(1)

Again, to prove that the 72nd term is twice of 34th term.

Let find these two terms.

✡ 34th term ___

n=34

a(34) = a +(34-1)d

=a + 33d

= 5d +33d [ Taking the value of a from eq 1]

=38d

✡ 72nd term__

a=72

a(72) = a+(72-1) d

= a+71d

=5d+71d

= 72d

= 2(38d)

So, a(72) = 2a(34)

Hence, (proved)

✧ Thanks ✧