1.What is the sum of the first 20 terms of this sequence (5, 15, 25,...)?
2.What is the sum of the first 15 terms of this sequence (5, 9, 13,...)?
3.In an arithmetic series, find the sum of the first 20 terms if the first term is -12 and the common difference is -5.
4.Find the sum of the series 14+11+8+...+ -82
5. How many terms of the arithmetic 1. sequence (1,3,5,7,...) will give a sum of 961?
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Answer:
Step-by-step explanation:
1.
[tex]s_{n}= \frac{20}{2} (2(5) + (20 - 1)10 \\ = 10(10 + 19(10)) \\ = 10(10 + 190) \\ s_{20}= 10(200) = 2000[/tex]
2.
[tex]s_{n} = \frac{15}{2} (2(5) + (15 - 1)4) \\ = \frac{15}{2}(10 + 14(4)) \\ = \frac{15}{2} (10 + 56) \\ = \frac{15}{2} (66)[/tex]
[tex] = \frac{15}{2} \times \frac{66}{1} \\ = \frac{990}{2} \\ s_{15}= 495[/tex]
3.
[tex]s_{n} = \frac{20}{2} (2( - 12) + (20 - 1) - 5) \\ = 10( - 24 + 19( - 5)) \\ = 10 ( - 24 - 95) \\ s_{20}= 10( - 119) = - 1190[/tex]
4.
[tex] - 82 = 14 + (n - 1) - 3 \\ - 82 - 14 = 14 - 14( - 3n + 3) \\ - 96 = - 3n + 3 \\ - 96 - 3 = - 3n + 3 - 3 \\ - 99 = - 3n[/tex]
[tex] \frac{ - 99}{ - 3} = \frac{ - 3n}{ - 3} \\ 33 = n[/tex]
[tex]s_{n} = \frac{33}{2} (14 + ( - 82) \\ = \frac{33}{2} (14 - 82) \\ = \frac{33}{2} ( - 68)[/tex]
[tex] = \frac{33}{2} \times \frac{ - 68}{1} \\ = \frac{33 \times ( - 68)}{2} = \frac{ - 2244}{2} \\ s_{n}= - 1122[/tex]
5.
[tex]961 = \frac{n}{2}(2(1) + (n - 1)2) \\ 961= \frac{n}{2} (2 + 2n - 2) \\ 961 = \frac{n}{2}(2n)[/tex]
[tex]961 = {n}^{2} \\ \sqrt{961}= { \sqrt{n} }^{2} \\ 31 = n[/tex]