This is and arithmetic series withd = -6since you notice -6 is the difference between the first term and the second term etc.If you call the first term u1 and the nth term un, then u1 = 200 and un = 44.You now need to find how many terms (n) there are in this series. Use the following formula:un = u1 + (n - 1)d44 = 200 + (n - 1)(-6)-156 = -6n +66n = 162 → n = 27Now, you can use the formula for finding sum of an arithmetic series:Sn = n/2 (u1 + un)S27 = 27/2 (200 + 44) = 13.5 * 244 = 3294Hence, the sum is 3294.
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