Question

the sum of first ‘n’ terms of an arithemetic progression is given by the formula sn = 3n2 + n, then its 3rd term is​

Answer 1

Step-by-step explanation:

Given :-

The sum of first ‘n’ terms of an arithemetic progression is given by the formula Sn = 3n²+ n

To find :-

Find its 3rd tterm ?

Solution :-

Given that :

The sum of first ‘n’ terms of an AP is

Sn = 3n²+ n -------(1)

Put n = 1 in (1) then

=> S1 = 3(1)²+1

=> S1 = 3(1)+1

=> S1 = 3+1

=> S1 = 4

=> First term of the AP = 4

Now,

Put n = 2 in (1) then

=> S2 = 3(2)²+2

=> S2 = 3(4)+2

=> S2 = 12 +2

=> S2 = 14

=> Sum of first two terms = 14

=> First term + Second term = 14

=> 4+Second term = 14

=> Second term = 14-4

=> Second term = 10

Now we have

First term = a = 4

Second term = 10

Common difference ( d)= 10-4 = 6

Common difference = 6

Third term of the AP = a3

We know that

The general term of an AP = an = a+(n-1)d

=> a3 = 4+(3-1)6

=> a3 = 4+2(6)

=> a3 = 4+12

=> a3 = 16

Answer:-

The third term of the given AP for the given problem is 16

Used formulae:-

• The general term of an AP = an = a+(n-1)d
• a = First term
• d = Common difference
• n = number of tetms

Answer 2

Step-by-step explanation:

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