Advertisements
Advertisements
Question
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
Advertisements
Solution
t11 = 16 and t21 = 29
t1 = ?, d = ? and t34 = ?
tn = a + (n - 1) d
t11 = a + (11 - 1) d
16 = a + 10 d ......(1)
t21 = a + (21 - 1) d
29 = a + 20d .........(2)
Subtracting equation (1) and (2)
a + 20 d = 29
a + 10 d = 16
_________________
10 d = 13
d = `13/10`
d = 1.3
Substituting d = 1.3 in equation (1)
16 = a + 10 d
a + 10 (1.3) = 16
a + 13 = 16
a = 16 - 13
a = 3
t34 = 3 + (34 - 1) (1.3)
= 3 + 33(1.3)
= 3 + 42.9
t34 = 45.9
APPEARS IN
RELATED QUESTIONS
If the term of m terms of an A.P. is the same as the sum of its n terms, show that the sum of its (m + n) terms is zero
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
Find how many integers between 200 and 500 are divisible by 8.
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 7 − 3n
Find the sum of first n odd natural numbers
Find the sum 2 + 4 + 6 ... + 200
If numbers n – 2, 4n – 1 and 5n + 2 are in A.P., find the value of n and its next two terms.
Find the sum of all odd natural numbers less than 50.
Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
If `4/5 `, a, 2 are in AP, find the value of a.
The sum of the first n terms of an AP is given by `s_n = ( 3n^2 - n) ` Find its
(i) nth term,
(ii) first term and
(iii) common difference.
Write an A.P. whose first term is a and the common difference is d in the following.
a = 10, d = 5
If the sum of first p term of an A.P. is ap2 + bp, find its common difference.
If the sum of n terms of an A.P. be 3n2 + n and its common difference is 6, then its first term is ______.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
x is nth term of the given A.P. an = x find x .
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
The sum of A.P. 4, 7, 10, 13, ........ upto 20 terms is ______.
