Question

Find the 10th term of an AP: √2, 3√2, 5√2, 7√2...​

Answer 1

Answer:

The 10th term of A.P is 19√2.

Explanation:

To find : 10th term of and AP.

We have A.P

• √2, 3√2, 5√2, 7√2...

So,

First term is √2

Second term is 3√2.

Common difference = Second term - First term

$\longrightarrow$ Common difference = 3√2 - √2

$\longrightarrow$ Common difference = 2√2

Common difference is 2√2.

We know,

General form of A.P is

a, a+d, a+2d, a+3d ...

[Where, a is first term and d is common difference]

And, if we want to find nth term of AP than formula is ,

$\bigstar \sf \: a_{n} = a + (n - 1)d$

[N is nth terms]

Now, Put a and d in formula :

$\longrightarrow \sf \: a_{10}$ = √2 + (10 - 1) × 2√2

$\longrightarrow \sf \: a_{10}$ = √2 + (9) × 2√2

$\longrightarrow \sf \: a_{10}$ = √2 + 18√2

$\longrightarrow \sf \: a_{10}$ = 19√2

Thus,

The 10th term of A.P is 19√2.

Answer 2

Solution :-

given AP series :- √2, 3√2, 5√2, 7√2

as we can see that,

→ First term = a1 = √2

→ Second term = a2 = 3√2

so,

→ common difference = d = a2 - a1 = 3√2 - √2 = 2√2

then,

→ T(n) = a + (n - 1)d , where a is first term and d is common difference .

putting values we get,

→ T(10) = √2 + (10 - 1)(2√2)

→ T(10) = √2 + 9 * 2√2

→ T(10) = √2 + 18√2

since √2 can be written as 1√2

therefore,

→ T(10) = √2(1 + 18)

→ T(10) = √2 * 19

→ T(10) = 19√2 (Ans.)

Hence, the 10th term of given AP is 19√2 .

Extra Knowledge :-

• A sequence is said to be in AP (Arithmetic Progression), if the difference between its consecutive terms are equal.

• The nth term of an AP is given as :-

• T(n) = a + (n-1)d , where a is the first term and d is the common difference.

• The common difference of an AP is given as :-

• d = T(n) - T(n-1)

• The sum up to nth terms of an AP is given as :-

• S(n) = (n/2)[2a + (n - 1)d]

• The nth term of an AP is also given as :-

• T(n) = S(n) - S(n - 1)

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