Question

Find the following :
If Sn=3n-1 find a3.

Answer 1

Answer:

$\large\boxed{\star\:\:\:a_3=10\:\:\:\star}$

Step-by-step explanation:

✢Given:-

   Sₙ=3n-1

✢To Find:-

a₃(3rd Term of its A.P.)

✢Formula Applied:-

• aₙ=a+(n-1)d

✢Solution:-

   Sₙ=3n-1

when n=1,

S₁=3×(1)-1

S₁=3-1

S₁=a=2

→a=2

When n=2,

S₂=3(2)-1

S₂=9-1

→S₂=8

S₂=a₁+a₂

8=2+a₂     [∵a₁=a=2 and S₂=8]

a₂=8-2

→a₂=6

d=a₂-a₁

d=6-2

→d=4

Now, we have to Find a₃:-

aₙ=a+(n-1)d, where a=2, n=3, d=4.

⇒a₃=2+(3-1)×4

⇒a₃=2+(2×4)

⇒a₃=2+8

$\implies\boxed{a_3=10}$