Question

What is the Sum of 10terms of the AP root 3,root 12, root 27.....

Answer 1

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Answer 2

Concept

An arithmetic progression is a sequence of numbers in which the common difference between any two numbers is constant. The sum of the first n terms of an AP is calculated as-

sum = n/2 [2a + (n-1)d]

where, a = first term

d = common difference

and n = number of terms

Given

An arithmetic progression-

$\sqrt{3} , \sqrt{12} , \sqrt{27} ,...$

Find

we need to find the sum of the first 10 terms of the given AP

Solution

We have

$\sqrt{3} , \sqrt{12} , \sqrt{27} ,...$

here, a = $\sqrt{3}$

and d = $\sqrt{12} - \sqrt{3}$

= $2\sqrt{3} - \sqrt{3}$

= $\sqrt{3}$

Now we know the formula for the sum of an AP is given by

sum = n/2 [2a + (n-1)d]

here n = 10

Thus, substituting the value of n, a, and d, we get

10/2 [ 2$\sqrt{3}$ + (10 - 1)$\sqrt{3}$]

= 5[ 2$\sqrt{3}$ + 9 $\sqrt{3}$]

= 5[ 11$\sqrt{3}$]

= 55$\sqrt{3}$

Hence, the sum of 10 terms of the given AP is 55$\sqrt{3}$.

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