# Find the R Th Term of an A.P., the Sum of Whose First N Terms is 3n2 + 2n. - Mathematics

Find the r th term of an A.P., the sum of whose first n terms is 3n2 + 2n.

#### Solution

$\text { Let a and d be the first term and the common difference of the given A . P . , respectively }$

$\text { As, } S_n = 3 n^2 + 2n$

$\text { So, } a = S_1 = 3 \times 1^2 + 2 \times 1 = 3 + 2 = 5 \text { and }$

$S_2 = 3 \times 2^2 + 2 \times 2 = 12 + 4 = 16$

$\Rightarrow a + a_2 = 16$

$\Rightarrow a + a + d = 16$

$\Rightarrow 2a + d = 16$

$\Rightarrow 2 \times 5 + d = 16$

$\Rightarrow d = 16 - 10$

$\Rightarrow d = 6$

$\text { Now },$

$a_r = a + \left( r - 1 \right)d$

$= 5 + \left( r - 1 \right) \times 6$

$= 5 + 6r - 6$

$\therefore a_r = 6r - 1$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.4 | Q 15 | Page 31