This page offers a step-by-step solution to the specific question **NCERT Class 11th Mathematics - Sequence and Series | the sum of the first four terms of an a p is 56 Answer ** from NCERT Class 11th Mathematics, Chapter Sequence and Series.

Question 12

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.

Answer

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

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

Sum of last four terms = [*a* + (*n* – 4) *d*] + [*a* + (*n* – 3) *d*] + [*a* + (*n* – 2) *d*] + [*a* + *n* – 1) *d*] = 4*a* + (4*n* – 10) *d*

According to the given condition,

4*a* + 6*d* = 56

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

⇒ 6*d* = 12

⇒ *d* = 2

∴ 4*a* + (4*n* –10) *d* = 112

⇒ 4(11) + (4*n* – 10)2 = 112

⇒ (4*n* – 10)2 = 68

⇒ 4*n* – 10 = 34

⇒ 4*n* = 44

⇒ *n* = 11

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

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Faujdar
2019-11-29 20:13:13

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Faujdar
2019-11-29 20:12:44

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Roya
2019-10-08 18:22:06

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Tushar Giri
2019-09-29 22:01:22

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Mohan
2019-09-19 09:55:18

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Tushar Gill
2019-01-19 07:14:27

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Tushar Gill
2019-01-19 07:14:04

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Mayank
2018-09-05 10:49:09

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2018-08-22 12:34:16

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Ishita
2018-08-22 12:33:53

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