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Find S10 for -1 + -7 + -13 + -19



i would greatly appreciate if you could give me the formula and do a step by step so i can use this as an example to help me with my other questions!!

Verified Answer :

texaschic101

first we find the common difference...to do this we subtract the first term from the second term. -7 - (-1) = -7 + 1 = -6

now we are going to find the 10th term
an = a1 + (n-1)d <== formula for finding any term in arithmetic series
a1 = 1st term, d = common difference, n = term we want to find
now we sub
a10 = -1 + (10 -1) -6
a10 = -1 + (9 * -6)
a10 = -1 - 54 
a10 = - 55

now we will find the sum
Sn = (n (a1+ an)) / 2 <== formula for finding the sum 
S10 = (10(-1 - 55))/2
S10 = (10(-56) / 2
S10 = -560/2
S10 = - 280

so the sum of the first 10 numbers is -280

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