Question

If a =2n then find the value of S3​

Answer 1

Answer- The above question is from the chapter 'Arithmetic Progressions'.

Please correct your question: It's aₙ= 2n

Given: aₙ=2n

To find: Sum of 3 terms

Solution: Put n= 1,2,3, ...

a₁= 2×1= 2

a₂= 2×2= 4

a₃= 2×3= 6

Given list of numbers= 2,4, 6, ...

d₁= 4-2= 2

d₂= 6-4= 2

∵d₁= d₂= 2

∴ Given list of numbers is an AP where a= 2 and d= 2.

S₃= n/2 [2a + (n-1)d]

S₃= 3/2 [2×2 + (3-1)2]

S₃= 3/2 [4+4]

S₃= 3/2 × 8

S₃= 3 × 4

∴ S₃= 12

Answer 2

The value of S₃ = 12

Correct question : If aₙ = 2n then find the value of S₃

Given :

aₙ = 2n

To find :

The value of S₃

Solution :

Step 1 of 2 :

Find first three terms of the progression

Here it is given that aₙ = 2n

Putting n = 1 , 2 , 3 we get

First term = a₁ = 2 × 1 = 2

Second term = a₂ = 2 × 2 = 4

Third term = a₃ = 2 × 3 = 6

Step 2 of 2 :

Find the value of S₃

S₃

= Sum of first three terms

= a₁ + a₂ + a₃

= 2 + 4 + 6

= 12

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