Advertisements
Advertisements
Question
An A.P. consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term of the A.P.
Advertisements
Solution
Given that,
a3 = 12
a50 = 106
We know that,
an = a + (n − 1)d
a3 = a + (3 − 1)d
12 = a + 2d ...(i)
Similarly, a50 = a + (50 − 1)d
106 = a + 49d ...(ii)
On subtracting (i) from (ii), we obtain
94 = 47d
d = 2
From equation (i), we obtain
12 = a + 2(2)
a = 12 − 4
a = 8
a29 = a + (29 − 1)d
a29 = 8 + (28)2
a29 = 8 + 56
a29 = 64
Therefore, 29th term is 64.
APPEARS IN
RELATED QUESTIONS
Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22
The ratio of the sum use of n terms of two A.P.’s is (7n + 1) : (4n + 27). Find the ratio of their mth terms
In an AP given a3 = 15, S10 = 125, find d and a10.
If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.
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 all odd numbers between 100 and 200.
Find the sum of the first 13 terms of the A.P: -6, 0, 6, 12,....
Find the sum of the first 15 terms of each of the following sequences having the nth term as
yn = 9 − 5n
If the numbers a, 9, b, 25 from an AP, find a and b.
Find the sum of all natural numbers between 200 and 400 which are divisible by 7.
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
The sequence −10, −6, −2, 2, ... is ______.
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
Find the sum of all 2 - digit natural numbers divisible by 4.
Find the sum \[7 + 10\frac{1}{2} + 14 + . . . + 84\]
If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is
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 \[\frac{S_1}{S_2} =\]
Let the four terms of the AP be a − 3d, a − d, a + d and a + 3d. find A.P.
Q.3
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
In an A.P. (with usual notations) : given d = 5, S9 = 75, find a and a9
The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.
If the nth term of an AP is (2n +1), then the sum of its first three terms is ______.
Find the value of a25 – a15 for the AP: 6, 9, 12, 15, ………..
Find the sum of all odd numbers between 351 and 373.
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
