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

2 thoughts on “find the next 5 terms and 14th term of an AP root2, root8, root18​”

1. Given:–

   • An A.P √2, √8, √18

   To Find:–

   • Next five Terms and 14th term

   Formula Used:–

   • [tex]{\boxed{\bf{a_n=a+(n-1)d}}}[/tex]

   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,

   [tex]\bf :\implies\:a_n=a+(n-1)d[/tex]

   Here, n = 14

   [tex]\sf :\implies\:a_14=\sqrt{2}+(14-1)\times \sqrt{2}[/tex]

   [tex]\sf :\implies\:a_14=\sqrt{2}+13 \sqrt{2}[/tex]

   [tex]\sf :\implies\:a_14=14\sqrt{2}[/tex]

   [tex]\bf :\implies\:a_14=\sqrt{392}[/tex]

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

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2. Answer:

   The next five terms for an AP is

   [tex] \sqrt{32} \\ \sqrt{50} \\ \sqrt{72} \\ \sqrt{98} \\ \sqrt{128} [/tex]

   Step-by-step explanation:

   [tex]the \: 14 \:th \: term \: of \: an \: ap \: is \: \sqrt{392} [/tex]

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