Question

If the sum of n terms of an A.P. is $2n^{2} + 5n$, then its nth term is
(a) 4n − 3
(b) 3n − 4
(c) 4n + 3
(d) 3n + 4

Answer 1

Answer:

nth term is  4n + 3

Among the given options option (c)  4n + 3 is correct.  

Step-by-step explanation:

Given :  

Sn = 2n² + 5n ………..(1)

On Putting n = 1 in eq 1,

S1 = 2(1)² + 5 × 1

S1 = 2 + 5

S1 = a1 = 7

On Putting n = 2 in eq 1,

S2 = 2(2)² + 5 × 2

S2 = 2 × 4 + 10

S2 = 8 + 10  

S2 = 18

⇒ a2 = S2 – S1  

⇒ a2 = 18 – 7  

⇒ a2 = 11

Common Difference ,d = a2 - a1

d = 11 - 7

d = 4

 

By using the formula ,nth term , an = a + (n - 1)d

an = 7 + (n –1) × 4

an  = 7 + (n –1)4

an = 7 + 4n - 4

an = 4n + 3

Hence, nth term is  4n + 3

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Given:

$s_{n} = 2n^{2} + 5n$

To find:

nth term of AP

Solution:

For n = 1

$s_{1} = 2 \times {1}^{2} + 5 \times 1 \\ \\ s_{1} =2 + 5 \\ \\ s_{1} =7$

$s_{1} = a_{1}$

For n = 2

$s_{2} = 2 \times {2}^{2} + 5 \times 2 \\ \\ s_{1} =2 \times 4 + 5 \times 2 \\ \\ s_{1} =8 + 10 \\ \\ s_{1} =18$

We know that,

$a_{n} = s_{n + 1} - s_{n } \\ \\ a_{2} = s_{2} - s_{1} \\ \\ a_{2} =18 - 7 \\ \\ a_{2} = 11$

$d = a_{2} - a_{1} \\ \\ d = 11 - 7 \\ \\ d = 4$

$a_{n} = a + (n - 1)d \\ \\ a_{n} =7 + (n - 1)4 \\ \\ a_{n} = 7 + 4n - 4 \\ \\ a_{n} =3 + 4n$

Option: c) 4n+ 3