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If the Sum of N Terms of an Ap is 2n2 + 3n, Then Write Its Nth Term. - Mathematics

If the sum of n terms of an AP is 2n2 + 3n, then write its nth term.

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Solution

Given: 

\[S_n = 2 n^2 + 3n\]

\[\Rightarrow S_1 = 2 \left( 1 \right)^2 + 3\left( 1 \right)\]

\[ = 5\]

\[ S_2 = 2 \left( 2 \right)^2 + 3\left( 2 \right)\]

\[ = 14\]

\[ \therefore a_1 + a_2 = 14\]

\[ \Rightarrow 5 + a_2 = 14\]

\[ \Rightarrow a_2 = 9\]

Common difference, d  = \[a_2 - a_1\] = 9  \[-\] 5  =  4
nth term = a + \[\left( n - 1 \right)d\]  = 5+\[\left( n - 1 \right)\]4
               = 4n+1

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Q 3 | Page 50
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