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Sia ? 6 years, 5 months ago
The formula to find the sample mean is: = ( Σ xi ) / n
The mode is the value that occurs the most often in a data set, and the range is the difference between the highest and lowest values in a data set.
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Sia ? 6 years, 5 months ago
an = n2 - 1
Put n = 1, 2, 3, 4, ..... we get,
a1 = 12 - 1 = 1 - 1 = 0
a2 = 22 - 1 = 4 - 1 = 3
a3 = 32 - 1 = 9 - 1 = 8
a4 = 42 - 1 = 16 - 1 = 15, and so on.
Hence, the given sequence is 0, 3, 8, 15
a2 - a1 = 3 - 0 = 3
a3 - a2 = 8 - 3 = 5
As a2 - a1 {tex} \ne {/tex} a3 - a2, the given sequence is not an AP.
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Sia ? 6 years, 3 months ago
According to question, we are given a triangle ABC in which AC2 = AB2 + BC2.
We need to prove that {tex}\angle B=90^{\circ}{/tex}
To start with, we construct a {tex}\Delta \mathrm{PQR}{/tex} right angled at Q such that PQ = AB and QR = BC.

Now, we observe that from {tex}\Delta{/tex}PQR, we have :
PR2 = PQ2 + QR2 (Pythagoras Theorem, as {tex}\angle Q=90^{\circ}{/tex})
PR2 = AB2 + BC2 ..................(i) (By construction)
But, AC2 = AB2 + BC2 ...............(ii) (given)
Therefore, AC = PR ................(iii) [From (i) and (ii)]
Now, in {tex}\Delta{/tex}ABC and {tex}\Delta{/tex}PQR,
AB = PQ (By construction)
BC = QR (By construction)
AC = PR [proved in (iii) above]
Therefore, {tex}\Delta ABC \cong \Delta PQR{/tex} (SSS congruence)
Hence, {tex}\angle{/tex}B = {tex}\angle{/tex}Q
But {tex}\angle{/tex}Q = {tex}{90^ \circ }{/tex} (By Construction)
Therefore, {tex}\angle{/tex}B = {tex}{90^ \circ }{/tex}
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You can check NCERT Solutions here : https://mycbseguide.com/ncert-solutions.html
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?Niharika Sharma ? 6 years, 5 months ago
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