Question

If the sum of n terms of an A.P. be $3n^{2} + n$ and its common difference is 6, then its first term is
(a) 2
(b) 3
(c) 1
(d) 4

Answer 1

Answer:

Its first term is 4.  

Among the given options option (d) 4 is correct.  

Step-by-step explanation:

Among the given options option (d) 4 is correct.  

Given :  

Sum of n terms of an AP, Sn = 3n² + n and common difference , d = 6

 

On putting n = 1 in Sn,  

Sn = 3n² + n

S1 = 3(1)² + 1  

S1= 3 + 1

S1 = 4

 

Sum of first term, S1 = first term ,a  = 4

S1 = a = 4  

Hence, its first term is 4.  

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer: Option - a [ 4 ]

EXPLANATION:

GIVEN :

Sum of n terms of an AP = 3n² + n

Common Difference = 6

We know that,

Sum of terms, Sn = n/2 [ 2a + (n - 1)d]

3n² + n = n/2 [ 2a + (n - 1)6 ]

3n² + n = n [ a + 6n - 6 ]

n [ 3n + n ] = n [ a + 6n - 6 ]

3n + n = a + 6n - 6

4n - 6n = a - 6

-2n = a - 6

Let n = 1

=> -2 = a - 6

=> -2 + 6 = a

=> a = 4

Therefore, the first term is 4.