Question

if an ap an=2n-1 then the product of first three terms is​

Answer 1

Nth term of an AP is generally given by Tn=a+(n-1)d. Now here it is given that Tn=2n+1. So,

a+(n-1)d=2n+1

a+nd-d=2n+1

nd+(a-d)=2n+1

Now comparing LHS and RHS,we get

d=2 and a-d=1

a-2=1

a=3.

So now sum of first 3 terms is given by

Sn=n/2(a+a+(n-1)d)

S3=3/2*(3+3+(3–1)2)

S3=3/2*10

S3=15

Therefore sum of frist three terms is 15.

Hope this will help you

Answer 2

The product of the first three numbers in an A.P is 15.

Given,

The $n^{th}$ term an AP is 2n-1

To Find,

The product of the first three terms.

Solution,

Here, given that in the A.P the $n^{th}$ term is (2n-1)

aₙ  = 2n-1.

Therefor,

a₁ = (2× 1 - 1)

a₁ = 2-1

a₁ = 1.

a₂ = (2× 2 -1)

a₂ = 4-1

a₂ = 3.

a₃ = (2 × 3 - 1)

a₃ = 6- 1

a₃ = 5.

So, the first three terms in the given A.P are 1, 3, and 5.

Therefore, the product result of those numbers.

1×3×5 = 15.

Hence, in an A.P whose $n^{th}$ term is (2n-1), the product of the first three numbers is 15.