Advertisements
Advertisements
Question
Write the formula of the sum of first n terms for an A.P.
Advertisements
Solution
Sum of the first n terms is given by
`S_n = n/2[2a + (n - 1)d]`,
where a = first term,
d = common difference
OR
`S_n = n/2(t_1 + t_n)`,
where t1 = first term,
tn = last term
APPEARS IN
RELATED QUESTIONS
Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120
Find the sum of first 30 terms of an A.P. whose second term is 2 and seventh term is 22
In an AP given d = 5, S9 = 75, find a and a9.
A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
If (m + 1)th term of an A.P is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...
Find the sum of the first 40 positive integers divisible by 3
Find the middle term of the AP 6, 13, 20, ..., 216.
Find the value of x for which the numbers (5x + 2), (4x – 1) and (x + 2) are in AP.
How many terms of the A.P. 21, 18, 15, ... must be added to get the sum 0?
Write an A.P. whose first term is a and common difference is d in the following.
a = –3, d = 0
Write an A.P. whose first term is a and common difference is d in the following.
Find four consecutive terms in an A.P. whose sum is 12 and sum of 3rd and 4th term is 14.
(Assume the four consecutive terms in A.P. are a – d, a, a + d, a +2d)
If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].
The sum of third and seventh term of an A. P. is 6 and their product is 8. Find the first term and the common difference of the A. P.
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 =
An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installment is Rs. 100 less than the previous one, find:
- amount of installments paid in the 9th month.
- total amount paid in the installment scheme.
Q.5
In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.)
