The sum of five terms of an arithmetic progression is 70. The product of the extreme terms is 132. Find the five terms.a.8, 12, 16, 20, 24b.10, 12, 14, 16, 18c.4, 8, 12, 16, 20d.6, 10, 14, 18, 22
Question
The sum of five terms of an arithmetic progression is 70. The product of the extreme terms is 132. Find the five terms.a.8, 12, 16, 20, 24b.10, 12, 14, 16, 18c.4, 8, 12, 16, 20d.6, 10, 14, 18, 22
Solution
The problem states that the sum of five terms of an arithmetic progression (AP) is 70 and the product of the extreme terms is 132.
Let's denote the five terms of the AP as a-d, a-c, a, a+c, a+d.
The sum of these five terms is given by the formula 5a = 70, so a = 14.
The product of the extreme terms is given by (a-d)(a+d) = 132. Substituting a = 14, we get (14-d)(14+d) = 132.
Solving this equation for d, we get d = 6.
Therefore, the five terms of the AP are 14-6, 14-3, 14, 14+3, 14+6, which are 8, 11, 14, 17, 20.
However, these terms are not in the given options. There might be a mistake in the problem or the options.
Similar Questions
Three terms are in arithmetic progression such that their sum is 36 and product is 1296. Find the three terms.a.4, 12, 20b.9, 12, 15c.8, 12, 16d.6, 12, 18
Find the sum of the first 20 terms of an arithmetic progression, if its fifth term is 11 and its 16th term is 39.
Find the 10th term of the arithmetic progression whose 4th term is 7 and whose 17th term is 72.a.42b.47c.32d.37
The ratio of the fifth term to the twelfth term of a sequence in an arithmetic progression is 6/13. If each term of this sequence is positive, and the product of the first term and the third term is 32, find the sum of the first 100 terms of this sequence.
Find the number of terms and the sum of the terms of the arithmetic progressions 32,28,….4a.7 : 126b.15 : 270c.14 : 252d.8 : 144
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.