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If sn, the sum of the first n terms of an AP, by sn=5n^2+3n, then find its its nth term. Pls ans

Posted by Priya Dharshini ? 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let a_n be the n ^th term of the A.P. Then,
a_n = S_n - S_n-1
{tex}\Rightarrow{/tex} a_n= (5n² + 3n) - {5(n -1)² + 3 (n- 1)} {tex}\left[ \begin{array} { l } { \text { Replacing } n \text { by } ( n - 1 ) \text { in } S _ { n } } \\ { \text { to get } S _ { n - 1 } = 5 ( n - 1 ) ^ { 2 } + 3 ( n - 1 ) } \end{array} \right]{/tex}
{tex}\Rightarrow{/tex}a_n = (5n² + 3n) - {5(n² - 2n+ 1) + 3n - 3}
{tex}\Rightarrow{/tex} a_n = (5n² + 3n) - {5n² -10n + 5 + 3n - 3}
{tex}\Rightarrow{/tex} a_n = (5n² + 3n) - (5n² - 7n + 2)
{tex}\Rightarrow{/tex} a_n = 10n - 2

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