Question

In an AP Sn=3n+5then the value of d is___​

Answer 1

Step-by-step explanation:

It is given that sn=3n+5 so let me the first term be a and common difference be d.

s1=3(1)+5

=3+5=8

a1=a=8

s2=3(2)+5

=6+5=11

a1+a2=11

therefore 8+a2=11

a2=11-8

a2=3

d=a2-a1

=3-8= - 5

so the value of d is - 5

Answer 2

Answer:

$sn = 3n + 5 \\ third \: term = s3 - s2 \\ = 3 \times 3 + 5 -( 3 \times 2 + 5) \\ = 9 + 5 - (6 + 5) \\ = 14 - 11 \\ = 3 \\ third \: term \: = 3 \\ fourth \: term = s4 - s3 \\ = 3 \times 4 + 5 - (3 \times 3 + 5) \\ = 17 - 14 \\ = 3 \\ fourth \: term = 3$

$third \: term = a + 2d = 3 \\ fourth \: term = a + 3d = 3 \\ subtracting \: both \: the \: equations \\ a + 3d - a - 2d = 3 - 3 \\ d = 0$