Question

In an AP, Sn=3n+5 then, the value of ‘d’ is:​

Answer 1

Step-by-step explanation:

Sn = n/2 ( 2a +(n-1) d)

2(3n+5) = n ( 2a +nd - d )

6n + 10 = 2an + n²d - nd

6n -2an + 10 = nd( n - 1 )

n(3-2a) = nd ( n-1 ) -10

3-2a = d(n-1) -10

d= (13 -2a) / n-1

Answer 2

Answer:

      d = -5

Step-by-step explanation:

Given :- In an AP, Sn=3n+5 then, the value of ‘d’ is:

Solution :-

→ Sn = 3n + 5

so,

at n = 1,

→ S1 = 3*1 + 5 = 3 + 5 = 8

at n = 2

→ S2 = 3*2 + 5 = 11

Let first term of given AP is a and common difference is d .

so,

→ S1 = a1 = 8

→ S2 = a1 + a2

→ S2 = a1 + (a1 + d)

then,

→ a1 + (a1 + d) = 11

→ 8 + 8 + d = 11  

→ 16 + d = 11

→ d = 11 - 16

→ d = (-5) (Ans.)