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

MST thank

Faujdar
2019-11-29 20:12:44

Mst

Roya
2019-10-08 18:22:06

Nice very helpful

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

Thank you so much

Mohan
2019-09-19 09:55:18

Tuð

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

Thanks its very helpful

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

Thanks its very helpful

Mayank
2018-09-05 10:49:09

Good

Ishita Sharma
2018-08-22 12:34:16

You have been doing a great job. Each step has been explainedc so well. I am really very much thankful to you

Ishita
2018-08-22 12:33:53

You have been doing a great job. Each step has been explainedc so well. I am really very much thankful to you

- NCERT Chapter