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Question

In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?

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Solution

Let the 1st term of A.P is =a
Ans the common difference is =d
Given, T5th=30=a+4d.....(1)
T12th=69=a+11d.....(2)
Eqn (2)(1)
35=7d
d=5
From Eqn (1)
30=a+4(5)
a=10
Now, the sum of 1st20 terms =S20
S20=202[2a+(2a1d]
S20=202[2(10)+19(5)]
S20=1150

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