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sukhopar [10]
2 years ago
6

Please help with this

Mathematics
1 answer:
inysia [295]2 years ago
6 0

Answer:

S_{n}<em> = n² + 4n ; n = 11 </em>

Step-by-step explanation:

S_{n} = \frac{n}{2} [2 a_{1} + (n - 1)d]

~~~~~~~~~

a_{1} = 5

d = 7 - 5 = 2

S_{n} = \frac{n}{2} [ 2(5) + 2(n - 1)] = \frac{n}{2} ( 8 + 2n ) = 4n + n²

S_{n}<em> = n² + 4n</em>

n² + 4n = 165

n² + 4n - 165 = 0

(n + 15)(n - 11) = 0 ( n ≥ 0 ) ⇒ <em>n = 11</em>

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