Find the sum of the first n terms of the following arithmeti

Find the sum of the first n terms of the following arithmetic sequence. a_2 = -20, a_5 = -263; n = 10

Solution

Arithmetic progression :

an = a1 + (n-1)d

a2 = -20 ; -20 = a1 + (2-1)d

-20 = a1 +d ----(1)

a5 = -263 ; -263 = a1 + 4d ----(2)

equation 2 and 1 gives : -243 = 3d

d = -81

a1 = -20 +81 = 61

an = 61 +(n-1)(-81) = -81n +142

Sum = (a1 +an)/2