You can put this solution on YOUR website! First, we start with three formulas:
This gives us the nth term of the arithmetic sequence.
SUM(n=1 to K) (constant) = K*constant
SUM(n=1 to k)(n) = k(k+1)/2.
We want SUM(n=1 to k) {A1 + 8n - 8}
this can be expressed as
SUM(n=1 to k) {A1} + SUM(n=1 to k) {8n} - SUM(n=1 to k) {8}
This gives us kA1 + 8(k)(K+1)/2 - 8k
Now
S21 = 21A1 + 4(21)(22) - 8(21) = 546
S22 = 22A1 + 4(22)(23) - 8(22) = 660
Subtracting the first from the second, we get
A1 + 176 - 8 = 114
A1 = -54.
Now, we have the formula for Tn as
Tn = -54 + 8(n-1)
The sum of the first 23 terms can be expressed as
SUM(n=1 to 23) {-54 + 8n - 8}
SUM(n=1 to 23) {-54} + SUM(n=1 to 23) {8n} - SUM(n=1 to 23) {8}
-54*23 + 8(23)(24)/2 - 8(23)
-1242 + 2208 -184 = 782.
S23 = 782.
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