Question

IN AN A.P.,THE SUM OF FIRST n TERMS IS 6n - n^2. WHAT IS THE 25th term?⚠️⚠️⚠️
answer with explanation

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Answer 1

Given sum of first n terms = 6n - n^2.

sn = 6n - n^2

Take n = 1:

= > s1 = 6(1) - 1^2 = 6 - 1 = 5

Take n = 2:

= > s2 = 6(2) - 2^2 = 12 - 4 = 8.

Here,

First term a1 = 5 and second term a2 = 8 - 5 = 3.

Common difference d = 3 - 5 = -2.

Now,

We know that nth term of an AP an = a + (n - 1) * d

= > a25 = a + (25 - 1) * (d)

= > a25 = 5 + (24) * (-2)

= > a25 = 5 - 48

= > a25 = -43.

Therefore, 25th term = -43

Hope this helps!