Advertisements
Advertisements
प्रश्न
If the nth term of the A.P. 58, 60, 62, .... is equal to the nth term of the A.P. –2, 5, 12, …., find the value of n.
उत्तर
In the first A.P. 58, 60, 62, ....
a = 58 and d = 2
tn = a + (n – 1)d
⇒ tn = 58 + (n – 1)2 ...(i)
In the first A.P. –2, 5, 12, ....
a = –2 and d = 7
tn = a + (n – 1)d
`\implies` tn= –2 + (n – 1)7 ...(ii)
Given that the nth term of first A.P is equal to the nth term of the second A.P.
`\implies` 58 + (n – 1)2 = –2 + (n – 1)7 …[From (i) and (ii)]
`\implies` 58 + 2n – 2 = –2 + 7n – 7
`\implies` 65 = 5n
`\implies` n = 13
APPEARS IN
संबंधित प्रश्न
Find three numbers in A.P. whose sum is 24 and whose product is 440.
How many two digit numbers are divisible by 3?
Which term of the A.P. 3, 8, 13, 18, … is 78?
Find the sum of the two middle most terms of the A.P. `-(4)/(3), -1, -(2)/(3),...,4(1)/(3)`
Which term of the A.P. 53, 48, 43,… is the first negative term?
The sum of 5th and 7th terms of an A.P. is 52 and the 10th term is 46. Find the A.P.
If 8th term of an A.P. is zero, prove that its 38th term is triple of its 18th term.
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
The sum of three numbers in A.P. is 3 and their product is – 35. Find the numbers.
The sum of the first three terms of an A.P.is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.
