If the a sum n terms an AP is define 3n2+4n. mth term is 151 find the firstterm and the difference.

Question

ignou bca 1 sem Bcs-012 assignment  2012-13

Answer 1

"AP"=??? aritmatik progresshun ????

yu sae 3n2...??? yu meen 3*n^2 ????

need more klues

Answer 2

This looked really, really hard because I thought the formula for the sum applied only for 1 value of n. Then I realized that it was a general formula that held for any n, and the problem became much easier.

Since the sum of 1 term is 3 + 4, we know the first term is 7
Since the sum of 2 terms is 3x4 + 8 = 20, we know the 2nd term is 13 and the difference between terms is 6.
(151 - 7)/6 = 144/6 = 24, so 151 is the 25th term.

Let's check these answers by recalculating the sum of n terms.
The nth term is 7 + 6(n-1)
The average term for n terms is (7 + 7 + 6n - 6)/2 = 4 + 3n
The sum of n terms is = n times this average = 4n +3n^2, as given. Yep, looks right.