Question

plez answer both questions ​

Answer 1

Step-by-step explanation:

1)

---》 root 2 , root 8 , root 18 ,root 32 is a given sequence.

a= t1 = root 2, t2 = root 8 , t3 = root 18 , t4 = root 32

therefore,

d = root 8 - root 2 = root 6

d = root 18 - root 8 = root 10

d = root 32 - root 18 = root 14

here , the common difference of a given sequence is not equal. therefore given sequence is not A.P.

The given sequence is not A.P. ,

so we can not find next two terms.

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Answer 2

$\huge\mathbb\red{SOLUTION }$

$\mathbb\pink{ GIVEN \: SEQUENCE} \\ \\ 1) \sqrt{2} , \sqrt{8}, \sqrt{18} ,\sqrt{32} \\ \\ \bf\ here \\ \\ \sf\ a = \sqrt{2} \\ \sf\ a2 = \sqrt{8} \\ a3 = \sqrt{18} \\ \sf\ a4 = \sqrt{32} \\ \\ \underline{we \: know \: that} \\ \\ \sf\ \: d = second \: term - first \: term \\ \\ \sf\ a2 - a \implies\\ \\ \sf\ \: d = \sqrt{8} - \sqrt{2} = 2\sqrt{2} - \sqrt{2} = \sqrt{2} \\ \\ \sf\ a3 - a2 \implies \\ \\ \sf\ \sqrt{18} - \sqrt{8} = 3 \sqrt{2} - 2 \sqrt{2} = \sqrt{2} \\ \\ a4 - a3 \implies \\ \\\sf\ \sqrt{32} - \sqrt{18} = 4 \sqrt{2} - 3 \sqrt{2} = \sqrt{2} \\ \\ \red{ \boxed{ \underline{d = \sqrt{2} \: \: \: \ddot\smile}}} \\ \\ \sf\ \therefore \: so \: next \: 2 \: terms \implies \: a5 \: and \: a6 \\ \\ here \\ a = \sqrt{2} \: and \: d = \sqrt{2} \\ \\ \sf\ \: a5 = a + 4d \\ \\ \sf\ \: \: \: \: \: \: = \sqrt{2} + 4 \times \sqrt{2} \\ \\ \sf\ \: \: \: \: \: \: = \sqrt{2} + 4 \sqrt{2} \\ \\ \sf\ \: \: \: \: \: = 5 \sqrt{2} = \sqrt{50} \\ \\ \sf\ \: a6 = a + 5d \\ \\ \sf\ \: \: \: \: \: = \sqrt{2} + 5 \times \sqrt{2} = 6 \sqrt{2} = \sqrt{72} \\ \\ \\.$

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$2)\sf\ {2}^{nd} \: term = 10 \\ \\ \sf\ {6}^{th} \: term = \frac{ {4}^{th} }{12} \\ \\\bf\ now \\ \\\sf\ a + d = 10 - - - - - - (1)\\ \\ \sf\ \: a + 5d = \frac{a + 3d}{12} \\ \\ \sf\ \implies: a + 3d = 12a + 60d \\ \\ \sf\ \implies: 12a - a + 60d - 3d \\ \\ \sf\ \implies: 11a + 57d = 0 \\ \\ \sf\ \implies: a = \frac{ - 57d}{11} - - - - - (2) \\ \\ \sf\ \bigstar \: now \: value \: of \: a \: put \: in \: 1 \\ \\ \sf\ \implies: \frac{ - 57d}{11} + d = 10 \\ \\ \sf\ \implies: \frac{ - 57d + 11}{11} = 10 \\ \\ \sf\ \implies: - 57d + 11 = 110 \\ \\ \sf\ \implies: - 57d = 110 - 11 \\ \\ \sf\ \implies: - 57d = 99 \\ \\ \sf\boxed{ \implies: d = \frac{99}{ - 57} = \frac{33}{ - 19} } \\ \\ \bf\underline{ value \: of \: d \: put \: in \: 2} \\ \\ a = \frac{ - 57 \times \frac{33}{ - 19} }{11} \\ \\ \sf\ \implies: \frac{ - 3 \times 33}{11} \\ \\ \sf\ \implies: a = - 3 \times 3 \\ \\ \sf\boxed{ \red{ \implies: a = - 27}}$