Arithmetic Progressions Test

Result

Arithmetic Progressions Test - 4

Score
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Rank
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Weekly Quiz Competition

Question 1
1 / -0

If a, b, c, d, e and f are in AP, then find the value of e - c.

A
2(c - a)

B
2(d - c)

C
2(f - d)

D
(d - c)

Solution

Since a, b, c, d, e and f are in AP.
Let common difference be x.

1^st term = a
2^nd term = b = a + x
3^rd term = c = a + 2x
4^th term = d = a + 3x
5^th term = e = a + 4x

e – c = a + 4x – (a + 2x) = a + 4x – a – 2x = 2x
Also, 2(d – c) = 2(a + 3x – a – 2x) = 2x
Question 2
1 / -0

A chocolate factory produced 5400 chocolates in the 7^th month and 7000 chocolates in the 11^th month of the year. Assuming that the production increased uniformly by a fixed number every month, how many chocolates were produced in one year?

A
62,400

B
64,200

C
62,500

D
62,000

Solution

T₇ = 5400

T₁₁ = 7000

T₇ = a + 6 × d

T₁₁ = T₇ + 4d

7000 = 5400 + 4 × d; d = 400;

T₇ = a + 6 × 400

5400 = a + 2400

a = 3000
Production in 1 year = S₁₂ = 12/2(2 × a + 11d) = 6(2 × 3000 + 11 × 400) = 62,400