Question

If the first term of AP is 3n²-4n then find the first term and common diffrence.​

Answer 1

Answer:

common difference = 6

Step-by-step explanation:

first term a1

n = 1

this does not form AP

3n^2 - 4n should be the sum of n terms

$3 {n}^{2} - 4n \\ s1 = a = 3( {1)}^{2} - 4(1) \\ = 3 - 4 \\ = - 1 \\ s2 = 3( {2)}^{2} - 4(2) \\ = 3(4) - 8 \\ = 12 - 8 \\ = 4 \\ s3 = 3( {3)}^{2} - 4(3) \\ = 27 - 12 \\ = 15$

a = - 1

a2 = s2 - a1 = 4-(-1) = 4 + 1 = 5

a3 = s3 - s2 = 15 - 4 = 11

therefore the AP is

-1, 5, 11 ....

common difference = a2 - a1 = a3 - a2

5 - (-1) = 11 - 5

5 + 1 = 11 - 5

6 = 6

the common difference = 6

hope you get your answer