Find the sum of the arithmetic series given a1 = -23, d=-10 and n=7

S7=-371

Explanation:

S7 (the sum of the first seven terms) = - 371

To find S7 we use the formula: Sn = n/2 · (2a1 + (n-1) ·d)

In this example we have a1 = - 23, d = - 10, n = 7. After substituting these values into the above equation, we obtain:

Sn = n · (2a1 + (n-1) ·d)

S7 = 7/2 · (2· (-23) + (7-1) · (-10))

S7 = 7/2 · (-46+6· (-10))

S7 = 7/2 · (-46 + (-60))

S7 = 7/2 · (-106)

S7 = - 371