Find the sum: 7 + 4 + 1 + ... + ( 10 − 3 n )

Answer 1

It's an arithmetic series with first term (a) = 7, common difference (d) = -3 and n terms.

Sum is (n/2) [ 2a + (n-1) d] = (n/2) (14 -3 (n-1)) = (n/2) (17 - 3n)

Answer 2

7,4,1,-2,-5,,,,,,,,,,,(10-3n) This numerical sequence is an arithmetic progression

∑ⁿ_i=1(10-3i) = 7+4+1+ + + (10-3i) using the formula above:

∑ⁿ_i=1(10-3i) = ∑ⁿ_i=1 (10) - 3•∑ⁿ_i=1i =10n -3/2(1+n)n =( 20n-3n-3n² )/2=(17n -3n²)/2