Advertisements
Advertisements
Question
Find the middle term of the A.P. 213, 205, 197, ---, 37.
Solution
Here,
a = 213
d = 205−213 = −8
Let the number of terms in the given AP be n.
We know
an=a+(n−1)d
⇒37=213+(n−1)(−8)
⇒8(n−1)=176
⇒n−1=22
⇒n=23
Thus, there are 23 terms in the given AP.
So, the (`(23+1)/2`)th term, i.e. the 12th term, will be the middle term.
∴ a12=213+(12−1)(−8)
⇒a12=213−88
⇒a12=125
Thus, 125 is the middle term of the given AP
APPEARS IN
RELATED QUESTIONS
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`sqrt2, sqrt8, sqrt18, sqrt32 ...`
Write the next two terms of A.P. whose first term is 3 and the common difference is 4.
For an A.P., find S7 if a = 5 and d = 4.
If seven times the 7th term of an A.P. is equal to eleven times the 11th term, then what will be its 18th term?
Find the middle term(s) of an A.P. 9, 15, 21, 27, …, 183.
Choose the correct alternative answer for the following sub question
1, 4, 7, 10, 13, ... Next two terms of this A.P. are ______
Which of the following form an AP? Justify your answer.
1, 1, 2, 2, 3, 3,...
Verify that the following is an AP, and then write its next three terms.
`0, 1/4, 1/2, 3/4, ...`
For arithmetic progression, first term is – 8 and last term is 55. If sum of all these terms is 235, find the number of terms and common difference.
The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.
- If the first circular row has 30 seats, how many seats will be there in the 10th row?
- For 1500 seats in the auditorium, how many rows need to be there?
OR
If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after the 10th row? - If there were 17 rows in the auditorium, how many seats will be there in the middle row?
