Advertisements
Advertisements
Question
The first term of an A.P. is 5, the common difference is 3 and the last term is 80; find the number of terms.
Advertisements
Solution
Here, a = 5, d = 3, an = 80
Let the number of terms be n.
Then, we have:
\[a_n = a + \left( n - 1 \right)d\]
\[ \Rightarrow 80 = 5 + \left( n - 1 \right)3\]
\[ \Rightarrow 75 = \left( n - 1 \right)3\]
\[ \Rightarrow 25 = \left( n - 1 \right)\]
\[ \Rightarrow 26 = n\]
Thus, there are 26 terms in the given A.P.
RELATED QUESTIONS
In an A.P., if pth term is 1/q and qth term is 1/p, prove that the sum of first pq terms is 1/2 (pq + 1) where `p != q`
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference.
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?
A sequence is defined by an = n3 − 6n2 + 11n − 6, n ϵ N. Show that the first three terms of the sequence are zero and all other terms are positive.
Let < an > be a sequence. Write the first five term in the following:
a1 = 1 = a2, an = an − 1 + an − 2, n > 2
Which term of the sequence 24, \[23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}\]....... is the first negative term?
Find the second term and nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
How many numbers of two digit are divisible by 3?
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
Find the sum of all odd numbers between 100 and 200.
Find the sum of all even integers between 101 and 999.
Find the sum of all integers between 100 and 550, which are divisible by 9.
Solve:
25 + 22 + 19 + 16 + ... + x = 115
If 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 two digit numbers which when divided by 4, yields 1 as remainder.
Find the sum of odd integers from 1 to 2001.
If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their 18th terms.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
Show that x2 + xy + y2, z2 + zx + x2 and y2 + yz + z2 are consecutive terms of an A.P., if x, y and z are in A.P.
A man saved Rs 16500 in ten years. In each year after the first he saved Rs 100 more than he did in the receding year. How much did he save in the first year?
A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?
Write the common difference of an A.P. the sum of whose first n terms is
If the sum of n terms of an AP is 2n2 + 3n, then write its nth term.
If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k =
If a, b, c are in G.P. and a1/x = b1/y = c1/z, then xyz are in
If a1, a2, ..., an are in A.P. with common difference d (where d ≠ 0); then the sum of the series sin d (cosec a1 cosec a2 + cosec a2 cosec a3 + ...+ cosec an–1 cosec an) is equal to cot a1 – cot an
A man saved Rs 66000 in 20 years. In each succeeding year after the first year he saved Rs 200 more than what he saved in the previous year. How much did he save in the first year?
Let 3, 6, 9, 12 ....... upto 78 terms and 5, 9, 13, 17 ...... upto 59 be two series. Then, the sum of the terms common to both the series is equal to ______.
The number of terms in an A.P. is even; the sum of the odd terms in lt is 24 and that the even terms is 30. If the last term exceeds the first term by `10 1/2`, then the number of terms in the A.P. is ______.
The internal angles of a convex polygon are in A.P. The smallest angle is 120° and the common difference is 5°. The number to sides of the polygon is ______.
