Week 2 – Arithmetic Sequence

S = t_1 + t_2 + t_3 + t_4 + t_5 + ….

t_1 = 143

Common Difference : -13

What is the term t_{253} and S_253 ?

* SOLUTION =>

t_1 = 143

t_2 = 143 + (-13) = 130

t_3 – 143 + (-13) + (-13) = 117

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t_253 = 143 + (-13) + (-13) + (-13) + ***

= 143 + (-13) x (n-1)

= 143 + (-13) x (253-1)

= 143 + (-13) x 252

= 143 + 3276

= 3419

S_1 = 143

S_2 = 143 + 143 + (-13) = 143 + 130 = 273

S_3 = 143 + 143 + (-13) + 143 + (-13) + (-13) = 143 + 130 + 117 = 390

S_4 = 143 + 143 + (-13) + 143 + (-13) + (-13) + 143 + (-13) + (-13) + (-13) = 494

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S_253 = 143 + 143 + (-13) + 143 + (-13) + (-13) + 143 + (-13) + (-13) + (-13) + *** + 143 + (-13) + (-13) + ***

= \frac{n}{2} x (143 + 3419)

= \frac{n}{2} x (3562)

= \frac{n} x 1781

= 253 x 1781

= 450593

In conclusion, t_253 = 3419 , S_253 = 450593.

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