Progressions & Series Test -2

Result

Progressions & Series Test -2

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

If a₁, a₂, a₃, ..... .is an A.P. such that a₁ + a₅ + a₁₀ + a₁₅ + a₂₀ + a₂₄ = 225 then a₁ + a₂ + a₃ + ...... + a₂₃ + a₂₄ is equal to-

A
909

B
75

C
750

D
900

Solution

We know that in an A.P. a₁+ a₂₄ = a₅ + a₂₀ + a₁₀ + a₁₅ = a₁₂ + a₁₃

So 3(a₁₂ + a₁₃) = 225 ⇒ a₁₂ + a₁₃ = 75

Therefore

a₁ + a₂ + a₃ + ………… + a₂₃ + a₂₄

= 12 (a₁₂ + a₁₃) = 12 × 75 = 900
Question 2
1 / -0

The sum of all even positive integers less then 200 which are not divisible by 6 is –

A
6534

B
6354

C
6543

D
6454

Solution

All even integer less than 200 is

2,4, 6, ………. 198 ⇒ n = 99

S₉₉ = 99/2 [2 + 198] = 9900

integer which are divisible by 6 is

6, 12, 18, ……….. 198 ⇒ n = 33

S₃₃ = 33/2 [6 + 198] = 33 × 102 = 3366

Sum of all integer which are not divisible by 6 is

= 9900 – 3366 = 6534