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Question 23. The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

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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 The first term of an A.P. is 5, the last term is 45 and the sum is 400.

Now we have to Find the number of terms and the common difference

CBSE DHANPAT RAI publication
CBSE Mathematics Class 10th
Question 23

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1 Answer

  1. Given A.P. has first term(a) = 5, last term(an) = 45 and sum(Sn) = 400.

    We know sum of n terms of an A.P. is given by, Sn = n[a + an]/2

    => 400 = n[5 + 45]/2

    => 50n = 800

    => n = 16

    Also, we know nth term of an A.P. given by, an = a + (n − 1)d.

    => 45 = 5 + (16 − 1)d

    => 15d = 40

    => d = 8/3

    Hence, the number of terms of given A.P. is 16 and common difference is 8/3.

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