Question

How many terms of the A.P. 9, 17, 25, .... must be taken to give a sum of 450?​

Answer 1

Hello !!

For you answer this question, you can just make use of this formula.

Sn = (n/2) × [2Ak + (n - k) × d]

Now, you put the information of the statement in the formula. Develop and find the result.

Sn = (n/2) × [2Ak + (n - k) × d]

450 = (n/2) × [2(9) + (n - 1) × (17 - 9)]

450 = (n/2) × [18 + (n - 1) × 8]

450 = (n/2) × [18 + 8n - 8]

450 = n(18 + 8n - 8)/2

450/1 = n(18 + 8n - 8)/2

n(18 + 8n - 8) = 450 × 2

n(18 + 8n - 8) = 900

18n + 8n^2 - 8n = 900

8n^2 - 8n + 18n = 900

8n^2 + 10n = 900

8n^2 + 10n - 900 = 0

Equation of second degree.

8n^2 + 10n - 900 = 0

Coefficients.

A = 8 ; B = 10 ; C = -900

Discriminant.

Δ = b^2 - 4ac

Δ = 10^2 - 4 × 8 × (-900)

Δ = 100 + 28800

Δ = 28900

Roots of the equation.

X = (-b ± √Δ)/2a

X = (-10 ± √28900)/2(8)

X = (-10 ± 170)/16

X' = (-10 + 170)/16

X' = 160/16

X' = 10 (it is the answer)

X'' = (-10 - 170)/16

X'' = (-180)/16

X'' = -45/4

Therefore, the answer is 10 terms.

I hope I have collaborated !