Question

The expressions for the sum to n terms of some
arithmetic sequences are given below. Find the
expression for the nth term of each:
)n square+ 2n​

Answer 1

Step-by-step explanation:

Given :-

Sum of the n terms of an AP is n²+2n

To find :-

Find the nth term of the AP ?

Solution :-

Given that :

Sum of the n terms of an AP is n²+2n

Sn = n²+2n -------------(1)

Put n = 1 in (1) then

=> S1 = (1)²+2(1)

=> S1 = 1+2

=> S1 = 3

=> First term = (a) = 3

Put n = 2 in (1) then

=> S2 = (2)²+2(2)

=> S2 = 4+4

=> S2 = 8

Sum of the two terms = 8

=> First term + Second term = 8

=>3+Second term = 8

=> Second term = 8-3

=> Second term = 5

Now,

Common difference (d) = 5-3 = 2

We know that

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

We have a = 3 and d = 2

On Substituting these values in the above formula then

an = 3+(n-1)(2)

=> an = 3+2n-2

=> an = 2n+(3-2)

=> an = 2n+1

So, nth term = 2n+1

Answer:-

The nth term of the given Arithmetic Progression is 2n+1

Used formulae:-

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

• a = First term

• d = common difference

• d = an - an-1

• an = nth term

• an-1 = (n-1)th term

• Sum of first n terms = Sn

• Sn = (n/2)[2a+(n-1)d]