Question

If sn=2n² +5n, then its n th term is
(a) 4n-3 (6) 3n-4(c) 4n+3 (d)3n+4​

Answer 1

Answer:

b. 3n-4

because

first term=7

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow s_n= 2n^2+5n$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow n^{th }\: term\:of\:an\:A.P$

✯FORMULA IN USE

$\large{\boxed{\bf{ \star\:\:a_n= a+(n-1)d \:\: \star}}}$

$\large\underline\bold{SOLUTION,}$

$\red{\text{first n terms of A.P,}}$

$\sf\therefore TAKING\:n=1$

$\sf\therefore S_n= 2n^2+5n$

$\sf\implies S_1= 2(1)^2+5(1)$

$\sf\implies S_n= 2+5$

$\sf\therefore S_n=7$

$\sf\dashrightarrow a_1=7\:-----[first\:term]$

$\sf\therefore TAKING\:n=2$

$\sf\dashrightarrow S_n= 2n^2+5n$

$\sf\implies S_n=2(2)^2+5(2)$

$\sf\implies S_n= 2(4)+10$

$\sf\implies S_n= 8+10$

$\sf\implies S_2=18$

FINDING, a_2,

$\sf\therefore a_1+a_2=S_2$

$\sf\implies 7+a_2=18$

$\sf\implies a_2=18-7$

$\sf\implies a_2=11$

$\large{\boxed{\bf{ a_2=11 }}}$

NOW, FINDING DIFFERENCE(d),

$\sf\therefore d= a_2-a_1$

$\sf\implies d= 11-7$

$\sf\implies d= 4$

$\large{\boxed{\bf{ difference(d)= 4}}}$

$\purple{\text{A.P= 7,11,15,19......,nth term}}$

$\sf\therefore a_n= a+(n-1)d$

$\sf\implies a_n=7 +(n-1)(4)$

$\sf\implies a_n= 7+ (4n-4)$

$\sf\implies a_n= 7+4n-4$

$\sf\implies a_n= 3+4n$

$\large{\boxed{\bf{ \star\:\:n^{th}\:term\:of\:an\:A.P=3+4n \:\: \star}}}$

$\large\underline\bold{n^{th}\:TERM\:OF\:AN\:A.P\:is\:3+4n}$

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