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# The Sum of the First Four Terms of an A.P. is 56. the Sum of the Last Four Terms is 112. If Its First Term is 11, Then Find the Number of Terms. - CBSE (Arts) Class 11 - Mathematics

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ConceptArithmetic Progression (A.P.)

#### Question

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

#### Solution

Let the A.P. be aa + da + 2da + 3d, ... a + (n – 2) da + (n – 1)d.

Sum of first four terms = a + (a + d) + (a + 2d) + (a + 3d) = 4a + 6d

Sum of last four terms = [a + (n – 4) d] + [a + (n – 3) d] + [a + (n – 2) d]

+ [a + n – 1) d]

= 4a + (4n – 10) d

According to the given condition,

4a + 6d = 56

⇒ 4(11) + 6d = 56 [Since a = 11 (given)]

⇒ 6d = 12

⇒ d = 2

∴ 4a + (4n –10) d = 112

⇒ 4(11) + (4n – 10)2 = 112

⇒ (4n – 10)2 = 68

⇒ 4n – 10 = 34

⇒ 4n = 44

⇒ n = 11

Thus, the number of terms of the A.P. is 11.

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 11 (2013 to Current)
Chapter 9: Sequences and Series
Q: 12 | Page no. 199
Solution The Sum of the First Four Terms of an A.P. is 56. the Sum of the Last Four Terms is 112. If Its First Term is 11, Then Find the Number of Terms. Concept: Arithmetic Progression (A.P.).
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