Question

the sum of a certain number of an AP series -8,-6.-4.,,,, is 52.the number of terms is

Answer 1

Answer:

16

Step-by-step explanation:

do you mean alternate route if yes then the answer will be

x+x+2+x+4+x+6=52

4x+12=52

x = (52-12)/4

x=10

therefore the biggest term is 16

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Answer 2

Step-by-step explanation:

-8 , -6 , -4...........

Here,

a = -8

d = -6 - (-8)

d = 2

To find :-

number of terms

Given :-

Sum = 52

Sn = n /2 ( 2a + (n - 1) × d )

52 = n/2 (2×-8 + (n - 1) × 2)

52 = n/2 (-16 + 2n - 2)

52 = n/2 (-18 + 2n)

52 = -9n + n²

n² - 9n - 52 = 0

Solving by Quadratic Equation ( middle term spilliting)

n² - 13n + 4n - 52 = 0

n(n - 13) +4 (n - 13) = 0

(n - 13) (n + 4) = 0

Therefore,

n - 13 = 0

n = 13

n + 4 = 0

n = -4

Since,

Term cannot be negative

Therefore,

n = 13

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