Advertisements
Advertisements
प्रश्न
Find the middle term of the AP 10, 7, 4, ……., (-62).
Advertisements
उत्तर
The given AP is 10,7,4,.....,-62.
First term, a = 10
Common difference, d = 7 -10 =-3
Suppose these are n terms in the given AP. Then,
an = -62
⇒10+ (n-1) × (-3) = -62 [ an = a + (n-1) d]
⇒ -3 (n-1) =-62 -10 = -72
⇒`n-1 = 72/3 = 24 `
⇒ n = 24 + 1= 25
Thus, the given AP contains 25 terms.
∴ Middle term of the given AP
=` ((25+1)/2) ` th term
= 13 th term
= 10+ (13-1) × (-3)
= 10-36
=-26
Hence, the middle term of the given AP is - 26.
APPEARS IN
संबंधित प्रश्न
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
A small terrace at a football field comprises 15 steps, each of which is 50 m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (See figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = `1/4 xx 1/2 xx 50 m^3`]
If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.
If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?
Find the sum of the first 40 positive integers divisible by 5
Find the sum of all multiples of 7 lying between 300 and 700.
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
For what value of n, the nth terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − kSn−1 + Sn−2, then k =
Find the sum of the first 10 multiples of 6.
For an A.P., If t1 = 1 and tn = 149 then find Sn.
Activitry :- Here t1= 1, tn = 149, Sn = ?
Sn = `"n"/2 (square + square)`
= `"n"/2 xx square`
= `square` n, where n = 75
If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are ______.
Find the sum of all the 11 terms of an A.P. whose middle most term is 30.
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
