Question

If the sum to n terms of a sequence is 2n² + 4. Find its nth term. Is this
sequence an A.P. ?​

Answer 1

Answer:

Given that sum of n terms of an ap is given by

$s(n) = 2 {n}^{2} + 4$

So,

$S_1 = 2 \times {1}^{2} + 4 \\ = 6 \\ \\ S_2 = 2 \times {2}^{2} + 4 \\ = 12 \\ \\ S_3 = 2 \times {3}^{2} + 4 \\ = 22 \\ \\ S_4 = 2 \times {4}^{2} \times 4 \\ = 36$

Now,

As we know that

$a_1 = S_1 = 6 \\ \\ a_2 = S_2 - S_1 \\ = 12 - 6 \\ = 6\\ \\ a_3 = S_3 - S_2 \\ = 22 - 12 \\ = 10 \\ \\ a_4 = S_4 - S_3 \\ = 36 - 22 \\ = 14$

So,

As we can't get an AP by these so the formula of sum of the AP is incorrect.

But we can see that exept first term all terms are in AP with first term 6 and common difference 4.

So,

nth term of the AP will be:-

4n+2 as :

$a_n = 6 + (n - 1)d \\ = 6 + 4n - 4 \\ = 4n + 2$

so, nth term of the given sequence will be

4n+2+6= 4n+6.

Answer 2

Answer:

No it is not true that the

sequence is not in AP .

so we can't find the nth term of the sequence as it does not form any particular sequence .

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