Question

The sum of the first n elements of an AP, 5n^2+2n, then its second element is
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Answer 1

Question :

The sum of the first n elements of an AP is 5n^2 + 2n , then find its second element .

Note:

• Ap is a type of sequence in which the difference between the consecutive terms are same.
• If the first term of an AP is a and the common difference of the AP is d then its nth term is given by;

T(n) = a + (n-1)d

• Also , for an AP the nth term is given by;

T(n) = S(n) - S(n-1)

• Also, the common difference for an AP is given by;

d = T(n) - T(n-1)

Solution:

Here,

It is given that the sum of the first n elements of an AP is 5n^2 + 2n.

Thus;

=> S(n) = 5n^2 + 2n

Also;

=> S(2) = 5(2)^2 + 2•2

=> S(2) = 5•4 + 2•2

=> S(2) = 20 + 4

=> S(2) = 24

And

=> S(1) = 5(1)^2 + 2•1

=> S(1) = 5•1 + 2•1

=> S(1) = 5 + 2

=> S(1) = 7

Now;

We know that;

For an AP the nth term is given by;

T(n) = S(n) - S(n-1)

Thus;

The 2nd term (element) of the AP will be given as;

=> T(2) = S(2) - S(2-1)

=> T(2) = S(2) - S(1)

=> T(2) = 24 - 7

=> T(2) = 17

Hence;

The second term of the AP is 17.