Advertisements
Advertisements
Question
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
Advertisements
Solution
Let the three times terms of an A.P. be (a - d ),a, (a + d)
sum = 42 = (a - d) + a + (a + d)
42 = 3a
⇒ ` a = 42/3`
⇒ a = 14
Also , (a - d ) (a + d) = 52
⇒ ` a^2 - d^2 = 52 `
`d^2 = a^2 - 52`
` = 196 - 52 `
`d^2 = 144`
⇒ `d = +- 12`
∴ First term ` = {(a - d,=,14,+,12,=,26),(a + d,=,14,-,12,=,2):}`
∴ A.P. is 2, 14, 26 or 26,14,2
APPEARS IN
RELATED QUESTIONS
If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S1)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the 10th, and the nth terms.
Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?
Find the sum of 28 terms of an A.P. whose nth term is 8n – 5.
If the sum of first p terms of an AP is 2 (ap2 + bp), find its common difference.
Choose the correct alternative answer for the following question .
In an A.P. 1st term is 1 and the last term is 20. The sum of all terms is = 399 then n = ....
If the common differences of an A.P. is 3, then a20 − a15 is
There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
Sum of 1 to n natural number is 45, then find the value of n.
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
