Answers to NCERT/CBSE MATHEMATICS Class 10(Class XI)textbook ... The
sum of the third and the seventh terms of an AP is 6 and their product is 8. Find.
NCERT/CBSE MATHEMATICS CLASS 10 textbook(OPTIONAL EXERCISE) http://www.TutorBreeze.com Contact for Online Tutoring in Physics, Math, Chemistry, English Answers to NCERT/CBSE MATHEMATICS Class 10(Class XI)textbook OPTIONAL EXERCISE CHAPTER FIVE
ARITHMETIC PROGRESSION EXERCISES
2. The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Solution: We know that the n th term of an Arithmetic Progression, whose First term = a and Common Difference = d is given by
(n - 1 ) d ∴ a3 = a + (3 - 1 ) d = a + 2 d a 7 = a + ( 7 - 1 ) d = a + 6d an = a +
The sum of the third and the seventh terms of an AP is 6 ⇒ a 3 + a 7 = ( a + 2 d ) + ( a + 6d ) = 6 ⇒ 2 a + 8d = 6 ⇒ a + 4d = 3 ⇒ a = 3 − 4d and the product of the third and the seventh terms of that AP is 8. ⇒ a 3 × a 7 = ( a + 2 d ) × ( a + 6d ) = 8 ⇒ ( a + 2 d ) × ( a + 6d ) = 8 ⇒ ( 3 − 4d + 2 d ) × ( 3 − 4d + 6d ) = 8 ⇒ ( 3 − 2d ) × ( 3 + 2d ) = 8 ⇒ 9 − 4d 2 = 8 ⇒ 4d 2 = 9 − 8 = 1
