Question

the sum of nth term of an arithmetic sequence is 2n^2-n

a)find the first term and common difference
b)write the sum of first 50terms​

Answer 1

1) n/2 [2a+(n-1)d] = 2n2 - n

cancel n from both sides and multiply 2

=> 2a + (n-1)d = 4n - 2

=> nd + (2a-d) = 4n - 2

now just compare the equations and equate

by comparing,

nd= 4n => d=4

2a-d= -2 => 2a-4= -2 => 2a=2=> a=1

2) just put 50 in place of n in the given equation as 2n2-n gives the sum for n terms

so sum= 50 (100-1)= 5000-50= 4950