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