Given that SR = 1+2+......+R Find S7+S4

Answer 1

SR = 1+2+3+...R

S7 = 1+2+3+4+5+6+7 = 28

sum of an arithmetic sequence of n terms = n(n+1)/2

it's an arithmetic sequence if each term has a common difference with the preceding term

it this case the common difference = 1 =2-1 = 3-2 = 4-3 = 5-4 = 6-5 = 7-6

SR = R(R+1)/2

S7 = 7(8)/2 = 28

S4 = 4(5)/2 = 10

S4+S7 = 10+28= 38