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# Question 20. 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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One of the most important and exam oriented question from Chapter name- Arithmetic Progression
Class 10th
Chapter number- 9
Exercise :- 9.6
This type of question has been asked in previous years exams.

In this question we have been given that in  an A.P., the 5th and 12th terms are 30 and 65 respectively,

Now we have to find out what is the sum of first 20 terms.

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 20

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1. Given A.P. has,

Fifth term, a5 = a + 4d = 30  …..(1)

Twelfth term, a12 = a + 11d = 65  ….(2)

On subtracting eq(1) from (2), we get,

=> (a + 11d) − (a + 4d) = 65 − 30

=> 7d = 35

=> d = 5

On putting d = 5 in eq(1), we get,

=> a + 4(5) = 30

=> a = 30 − 20

=> a = 10

We know sum of n terms of an A.P. is given by Sn = n[2a + (n − 1)d] / 2.

Here a = 10, d = 5 and n = 20. So we get,

S20 = 20[2(10) + (20 − 1)(5)]/2

= 20[20 + 95]/2

= 10[115] = 1150

Hence, the sum of first 20 terms for the given A.P. is 1150.

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