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Find the Sum of All Two Digit Numbers Which When Divided by 4, Yields 1 as Remainder. - Mathematics

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Question

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

Solution

The two-digit numbers, which when divided by 4, yield 1 as remainder, are

13, 17, … 97.

This series forms an A.P. with first term 13 and common difference 4.

Let n be the number of terms of the A.P.

It is known that the nth term of an A.P. is given by, an = a + (n –1) d

∴97 = 13 + (n –1) (4)

⇒ 4 (n –1) = 84

⇒ n – 1 = 21

⇒ n = 22

Sum of n terms of an A.P. is given by,

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 11 (2018 (Latest))
Chapter 9: Sequences and Series
Q: 6 | Page no. 199
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Solution Find the Sum of All Two Digit Numbers Which When Divided by 4, Yields 1 as Remainder. Concept: Arithmetic Progression (A.P.).
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