Question

if the sum of n term of series is (3n2-n) prove that the series is an AP also fine 1st term and common different​

Answer 1

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Answer:

FIRST TERM IS 2 and COMMON DIFFERENCE =6

Step-by-step explanation:

Given that,

Sum of n  terms(Sn)=3n²-n

So when we put n= 1,2,3,4.....

we get,

S(1)=3(1)²-1=2

S(2)=3(2)²-2=10

S(3)=3(3)²-3=24

S(4)=3(4)²-4=44

By using the formula,

an=S(n)-S(n-1)

Putting n=1,2,3,4 we get,

a1=S(1)-S(1-1)=S(1)=2

THEREFORE FIRST TERM IS 2.

a2=S(2)-S(2-1)=S(2)-S(1)=10-2=8

THEREFORE SECOND TERM IS 8.

a3=S(3)-S(3-1)=S(3)-S(2)=24-10=14

THEREFORE THIRD TERM IS 14.

Similarly, FOURTH TERM IS 20.

Here the difference  between the terms is common so the series is an AP

The common difference =a2- a1 =a3 - a2 = a4 - 3 = 6.

          THANKS  BUDDY  HAVE  A  NICE DAY          

Answer 2

Step-by-step explanation:

if the sum of n term of series is (3n2-n) prove that the series is an AP also fine 1st term and common different