Question

given Sn=2n²+3n
find a16

Answer 1

Hii There!!!


Given that, Sn = 2n^2 + 3n


Here, firstly we have to form an A.P

So, Taking n = 1

=> S1 = 2 (1) ^ 2 + 3× 1

=> S1 = 5

Since, sum of first term of an A.P is first term

So, a = 1 -------1)



Now,

Similarly, taking n= 2

S(2) = 2 × 2^2 + 3 × 2

=> S2 = 24



For finding 2nd term ----->>>

Sum of 2 terms is 14


So, 5 + a2 = 14

=> a2 = 14 - 5

=> a2 = 9 --------2)


Thus , A.P becomes, 5,9............


For Common difference, a2- a1 = 9- 5 = 4


Now, we have to find a16


So, by using formula ,

an = a + ( n - 1 ) × d


=> a16 = 1 + ( 16 - 1 ) × 4


=> a16 = 5 + 60


=> a16 = 65



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Hope it helps

Answer 2

given Sn = 2n^2 + 3n ----(1)

let n = 1,2,3....

put n = 1 in equation (1) , then ,

S 1 = 2 + 3 = 5

S 1= 5

sum of first term will be the first term , a1 = 5

put n = 2 in eq . (1), we get

S 2 = 8+ 6

S 2 = 14

S2 = a2 = 14

put n = 3 in eq.(1) , we get

S 3 = 18 + 9

= 27

S 3 = a3 = 27

now common difference

d = ( a 3 - a 2 ) - ( a2 - a1 )

d = ( 27 - 14 ) - ( 14 - 5 )

d = 13 - 9

d = 4

a1 = 5

now a16 = a1 + 15 d

a16 = 5 + 15 ( 4)

a16 = 5 + 60

a16 = 65

a16 = 65

therefore, a16 = 65