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Arithmetic Progressions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSArithmetic Progressions1 Mark
MCQ
If the sum of n terms of an A.P. is $2n^2 + 5 n$, then its nth term is
  • A
    4n − 3
  • B
    3n − 4
  • ✓
    4n + 3
  • D
    3n + 4
✓

Answer

Correct option: C.
4n + 3
  1. 4n + 3
Solution:
$\text{S}_\text{n}=2\text{n}^2+5\text{n}$
$\text{S}_1=2.1^2+5.1=8$
$\therefore\text{a}_1=7$
$\text{S}_2=2.2^2+5.2=18$
$\therefore\text{a}_1+\text{a}_2=18$
$\Rightarrow\text{a}_2=11$
Common difference, $\text{d}=11 -7 =4$
$\text{a}_\text{n}=\text{a}+(\text{n}-1)\text{d}$
$=7+(\text{n}-1)4$
$=4\text{n}+3$

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