Question

The sum of the first 50 common terms of 12,16,20,... and 18,24,30,....

Answer 1

series1 is every 4, series2 is every 5, so LCM is 20, so its 19, 39,59,79 

so 19+49*20= 19+980=999 

Avg*#of terms=sum, so 19+999/2 * 50 = 1018/2 * 50 = 509 * 50 = 25450 
D

Answer 2

1st AP Series : 12, 16, 20, ....

⇒ a1 = 12

⇒ d = 4

Find the nth series:

an = a1 + (n - 1)d

an = 12 + (n - 1)4

an = 12 + 4n - 4

an = 8 + 4n

Find the 50th term:

an = 8 + 4n

an = 8 + 4(50) = 208

Find the sum of the first 50 terms:

Sn = n/2 (a1 + an)

s50 = 50/2 (12 + 208) = 5500

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2nd AP Series : 18, 24, 30, ...

⇒ a1 = 19

⇒ d = 6

Find the AP series:

an = a1 + (n - 1)d

a50 = 19 + (50 - 1)(6)

a50 = 313

Sum of the 50 terms:

Sn = n/2 (a1 + an)

s50 = 50/2 (19 + 313) = 8300

Find the sum of the 50 terms in both series:

Sum = 5500 + 8300 = 13800

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Answer: 13800