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Katarina [22]
2 years ago
12

Please answer with clear instructions so that i can apply this to other questions.

Mathematics
1 answer:
kvv77 [185]2 years ago
7 0

Answer:

10 terms

Step-by-step explanation:

equate the sum formula to 55 and solve for n

\frac{1}{2} n(n + 1) = 55 ( multiply both sides by 2 to clear the fraction )

n(n + 1) = 110 ← distribute parenthesis on left side

n² + n = 110 ( subtract 110 from both sides )

n² + n - 110 = 0 ← in standard form

Consider the factors of the constant term (- 110) which sum to give the coefficient of the n- term (+ 1)

the factors are + 11 and - 10 , since

11 × - 10 = - 110 and 11 - 10 = + 1 , then

(n + 11)(n - 10) = 0 ← in factored form

equate each factor to zero and solve for n

n + 11 = 0 ⇒ n = - 11

n - 10 = 0 ⇒ n = 10

However, n > 0 , then n = 10

number of terms which sum to 55 is 10

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