Advertisements
Advertisements
Question
Find the middle term of the AP 6, 13, 20, …., 216.
Advertisements
Solution
The given AP is 6,13,20,........,216.
First term, a = 6
Common difference, d =13- 6 = 7
Suppose these are n terms in the given AP. Then,
an = 216
⇒ 6+(n-1) × 7 = 216 [ an = a + (n-1) d]
⇒ 7 (n-1) = 216 -6 =210
⇒ n-1`=210/7 =30`
⇒ n= 30+1 =31
Thus, the given AP contains 31 terms,
∴ Middle term of the given AP
`=((31+1)/2)`th term
= 16th term
= 6+ (16-1) × 7
= 6+105
=111
Hence, the middle term of the given AP is 111.
APPEARS IN
RELATED QUESTIONS
Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185
The sum of the first p, q, r terms of an A.P. are a, b, c respectively. Show that `\frac { a }{ p } (q – r) + \frac { b }{ q } (r – p) + \frac { c }{ r } (p – q) = 0`
Find the sum of the following APs.
`1/15, 1/12, 1/10`, ......, to 11 terms.
In an AP given l = 28, S = 144, and there are total 9 terms. Find a.
Find the sum of all 3 - digit natural numbers which are divisible by 13.
How many two-digits numbers are divisible by 3?
If (2p – 1), 7, 3p are in AP, find the value of p.
Write an A.P. whose first term is a and common difference is d in the following.
a = –19, d = –4
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.
If the sum of first p term of an A.P. is ap2 + bp, find its common difference.
If S1 is the sum of an arithmetic progression of 'n' odd number of terms and S2 the sum of the terms of the series in odd places, then \[\frac{S_1}{S_2} =\]
What is the sum of an odd numbers between 1 to 50?
If the nth term of an AP is (2n +1), then the sum of its first three terms is ______.
Find the sum:
`4 - 1/n + 4 - 2/n + 4 - 3/n + ...` upto n terms
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)
Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.
Reason (R): The sum of first n odd natural numbers is n2.
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.
