Question

Next term of the AP √2, 3√2, 5√2, ……. is
(a) 2√7
(6) 6√2
(c) 9√2
(d) 7√2​

Answer 1

Answer:

7√2

Step-by-step explanation:

$\red{\boxed{\rm Solution}}$

Given,

√2, 3√2, 5√2, ……. is an AP series

To find,

Next term, i.e fourth term of the given AP series

Solution,

From the given AP series,

a (First term) = √2

We know that common difference (d) can be found out by taking the difference between the second and first term of the AP series.

d (Common difference) = 3√2 - √2

We know that tn term in an AP series is given by,

$\rm t_n=a+(n-1)d$

Applying the above formula to find the fourth term,

Here we have to find fourth term so instead of n we have put 4 and we have to subtisute the values of a and d

$\to \rm t_4 = √2 + (4 - 1)(3√2 - √2)$

$\to \rm t_4 = √2 + 3(3√2 - √2)$

$\to \rm t_4 = √2 + 9√2 -3√2$

$\to \rm t_4 = \sqrt{2} (1 + 9 - 3)$

$\to \rm t_4 = √2(10 - 3)$

$\to \rm t_4 = 7 \sqrt{2}$

Hence the fourth term of the given AP series is 7√2

Hence option d is correct.

$\boxed{\rm t_4 = 7 \sqrt{2} }$

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Next term of the AP √2, 3√2, 5√2 …. is

(a) 2√7

(6) 6√2

(c) 9√2

(d) 7√2

CONCEPT TO BE IMPLEMENTED

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

EVALUATION

Here the given arithmetic progression is

√2, 3√2, 5√2, …

First term = a = √2

Second Term = 3√2

Third term = 5√2

Common Difference

= d

= 3√2 - √2

= 2√2

Hence the required next term of the AP

= 4th term of the AP

= a + 3d

= √2 + 6√2

= 7√2

FINAL ANSWER

Hence the correct option is (d) 7√2

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