What is the sum of the first 5 terms in the sequence?

For an A.P. with first term as a and common difference d , the sum up to n terms are given by ;

S(n) = (n/2)[2a + (n-1)d] . Here, n = 5 and S(n) = 60. Therefore,

60 = (5/2)[2a + 4d] = 5[a + 2d] or

a+2d = 12 , which is one equation for 2 unknowns, so let us take one of them, say a, as free variable, then 2d = 12 - a . Now, for different values of a, we get different values of d, thus giving out infinite different A.Ps. That is not an unique A.P. but many A.Ps.are possible. For instant, let a = 0 , then d = 6 and the A.P. with this data is : 0, 6, 12, 18, 24, …. .. . Similarly for a different value of a , you will be getting another A.P., different from the above one and so on .

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