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Sia ? 6 years, 4 months ago
According to the Pythagoras theorem, we can conclude that {tex}{\left( {\sqrt 5 } \right)^2} = {\left( 2 \right)^2} + {\left( 1 \right)^2}{/tex} We need to draw a line segment AB of 1 unit on the number line. Then draw a straight line segment BC of 2 units. Then join the points C and A, to form a line segment BC. Then draw the arc ACD, to get the number {tex}\sqrt 5 {/tex} on the number line.

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Sia ? 6 years, 4 months ago
We are given, an = 3n + 5 which is nth term.
So, a1 = 3(1) + 5 = 8
and, a2 = 3(2) + 5 = 6 + 5 = 11
so common difference, d = a2 - a1 = 11 - 8 = 3
Therefore common difference is 3
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According to the question,we are given that,
{tex}S _ { n } = \frac { 3 n ^ { 2 } } { 2 } + \frac { 5 n } { 2 } = \frac { 3 n ^ { 2 } + 5 n } { 2 }{/tex}
{tex}\Rightarrow S _ { n - 1 } = \frac { 3 ( n - 1 ) ^ { 2 } + 5 ( n - 1 ) } { 2 }{/tex}
{tex}= \frac { 3 \left( n ^ { 2 } - 2 n + 1 \right) + 5 n - 5 } { 2 }{/tex}
{tex}= \frac { 3 n ^ { 2 } - 6 n + 3 + 5 n - 5 } { 2 }{/tex}
{tex}= \frac { 3 n ^ { 2 } - n - 2 } { 2 }{/tex}
Now,
nth term = Tn=Sn-Sn-1={tex}= \frac { 3 n ^ { 2 } + 5 n } { 2 } - \frac { 3 n ^ { 2 } - n - 2 } { 2 } = \frac { 3 n ^ { 2 } + 5 n - 3 n ^ { 2 } + n + 2 } { 2 }{/tex}={tex}\frac{{6n + 2}}{2}{/tex}=3n+1
25th term=T25=3(25)+1=75+1=76.
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Piyush Shah 7 years, 3 months ago
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