Question

the sum of n term of the a.p. √2, √8, √18, √32,.......is

Answer 1

please please please tell me that thing

Answer 2

Sum of n terms of the a.p. is $\frac{n.(n+1)}{\sqrt{2} } .$

• A term which is called common difference is used in the case of arithmetic progressions and sequences. One example of sequence in real life is the commemoration of birthdays of individuals. In this instance, there is typically a one-year gap between consecutive celebrations of the same person.
• The difference between any term and its preceding term is an arithmetic sequence's is referred to as the common difference. An arithmetic sequence always adds (or subtracts) the same amount to go from one term to the next.
• The amount that is added (or removed) at each point in an arithmetic progression is referred to as the "common difference" because, if we subtract (that is, if we determine the difference of) succeeding terms, we will always arrive at this common value.

Here, according to the given information, we are given that,

The arithmetic progression is given as,

√2 + √8 + √18 + √32 + ...

Now, the A.P. can be re-written as,

$\sqrt{2}+2\sqrt{2} +3\sqrt{2} +4\sqrt{2} + ...$

Or, $\sqrt{2}(1+2+3+4,...)$

Then, the sum of the arithmetic progression is,

$\sqrt{2}. \frac{n.(n+1)}{2} \\=\frac{n.(n+1)}{\sqrt{2} } .$

Hence, sum of n terms of the a.p. is $\frac{n.(n+1)}{\sqrt{2} } .$

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