Question

find the next 5 terms and 14th term of an AP root2, root8, root18​

Answer 1

Answer:

The next five terms for an AP is

$\sqrt{32} \\ \sqrt{50} \\ \sqrt{72} \\ \sqrt{98} \\ \sqrt{128}$

Step-by-step explanation:

$the \: 14 \:th \: term \: of \: an \: ap \: is \: \sqrt{392}$

Answer 2

Given:-

• An A.P √2, √8, √18

To Find:-

• Next five Terms and 14th term

Formula Used:-

• ${\boxed{\bf{a_n=a+(n-1)d}}}$

Solution:-

Firstly,

• √2

• √8 = 2√2

• √18 = 3√2

So, the A.P can also be √2, 2√2, 3√3

Here,

• a = √2

• d = 2√2 - √2 = √2

For next five Terms,

• 4th term = 3√2 + √2 = 4√2 = √32

• 5th term = 4√2 + √2 = 5√2 = √50

• 6th term = 5√2 + √2 = 6√2 = √72

• 7th term = 6√2 + √2 = 7√2 = √98

• 8th term = 7√2 + √2 = 8√2 = √128

Hence, The next five Terms of the given A.P is √72, √50, √72, √98 and √128.

Now, For 14th term of an A.P,

$\bf :\implies\:a_n=a+(n-1)d$

Here, n = 14

$\sf :\implies\:a_14=\sqrt{2}+(14-1)\times \sqrt{2}$

$\sf :\implies\:a_14=\sqrt{2}+13 \sqrt{2}$

$\sf :\implies\:a_14=14\sqrt{2}$

$\bf :\implies\:a_14=\sqrt{392}$

Hence, The 14th Term of an A.P is √392.

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