Advertisements
Advertisements
प्रश्न
The 16th term of an AP is 1 more than twice its 8th term. If the 12th term of the AP is 47, then find its nth term ?
उत्तर
Let a be the first term and d be the common difference of the given A.P.
According to the given question,
16th term of the AP = 2 × 8th term of the AP + 1
i.e., a16 = 2a8 + 1
`a+(16-1)d=2[a+(8-1)d]+5` `thereforea_n=a+(n-1)d`
`rArra+15d=2[a+7b]+5`
`rArra+15d=2a+14d+5`
`rArrd=a+1 .............(1)`
Also, 12th term, a12 = 47
`rArra+(12-1)d=47`
`rArra+11d=47`
`rArra+11(a+1)=47` [Using(1)]
`rArra+11a+11=47`
`rArr12a=36`
`rArra=3`
On Putting the value of a in (1), we get d = 3 + 1 = 4
Thus, nth term of the AP, an= a + (n − 1)d
On putting the respective values of a and d, we get
an= 3 + (n − 1) 4 = 3 + 4n − 4 = 4n − 1
Hence, nth term of the given AP is 4n − 1.
APPEARS IN
संबंधित प्रश्न
Choose the correct choice in the following and justify:
11th term of the A.P. `-3, -1/2, 2,` ..., is ______.
Which term of the A.P. 3, 8, 13, 18, ..., is 78?
Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.
How many three-digit numbers are divisible by 7?
Reshma wanted to save at least Rs 6,500 for sending her daughter to school next year (after 12 month.) She saved Rs 450 in the first month and raised her savings by Rs 20 every next month. How much will she be able to save in next 12 months? Will she be able to send her daughter to the school next year?
What value is reflected in this question ?
The 11th term of the AP: `-5, (-5)/2, 0, 5/2, ...` is ______.
Two APs have the same common difference. The first term of one of these is –1 and that of the other is – 8. Then the difference between their 4th terms is ______.
Justify whether it is true to say that the following are the nth terms of an AP.
3n2 + 5
Fill in the blank in the following table, given that a is the first term, d the common difference, and an nth term of the AP:
| a | d | n | an |
| -18 | ______ | 10 | 0 |
Determine the A.P. whose third term is 5 and the seventh term is 9.
