Advertisements
Advertisements
Question
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
Advertisements
Solution
a + b, a − b, a − 3b ... to 22 terms
\[\text { We have }: \]
\[\text { First term } = a + b, d = \left( a - b - a - b \right) = - 2b\]
\[n = 22\]
\[ S_n = \frac{n}{2}\left[ 2a + (n - 1)d \right]\]
\[ = \frac{22}{2}\left[ 2 \times (a + b) + (22 - 1)( - 2b) \right]\]
\[ = 11\left[ 2a - 40b \right] = 22a - 440b\]
RELATED QUESTIONS
Find the sum to n terms of the A.P., whose kth term is 5k + 1.
The sums of n terms of two arithmetic progressions are in the ratio 5n + 4: 9n + 6. Find the ratio of their 18th terms
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
A man starts repaying a loan as first installment of Rs. 100. If he increases the installment by Rs 5 every month, what amount he will pay in the 30th installment?
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
The pth, qth and rth terms of an A.P. are a, b, c respectively. Show that (q – r )a + (r – p )b + (p – q )c = 0
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?
Show that the following sequence is an A.P. Also find the common difference and write 3 more terms in case.
3, −1, −5, −9 ...
Which term of the A.P. 84, 80, 76,... is 0?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely real ?
How many terms are there in the A.P. 7, 10, 13, ... 43 ?
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.
The 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.
Find the 12th term from the following arithmetic progression:
1, 4, 7, 10, ..., 88
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
Find the sum of first n natural numbers.
Find the sum of all even integers between 101 and 999.
If Sn = n2 p and Sm = m2 p, m ≠ n, in an A.P., prove that Sp = p3.
Find the sum of odd integers from 1 to 2001.
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1 : S2 = (2n + 1) : (n + 1).
If \[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P., prove that:
\[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P.
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.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
A man arranges to pay off a debt of Rs 3600 by 40 annual instalments which form an arithmetic series. When 30 of the instalments are paid, he dies leaving one-third of the debt unpaid, find the value of the first instalment.
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
If the sums of n terms of two AP.'s are in the ratio (3n + 2) : (2n + 3), then find the ratio of their 12th terms.
If the sum of n terms of an A.P. be 3 n2 − n and its common difference is 6, then its first term 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
If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − k Sn − 1 + Sn − 2 , 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 =
Mark the correct alternative in the following question:
\[\text { If in an A . P } . S_n = n^2 q \text { and } S_m = m^2 q, \text { where } S_r \text{ denotes the sum of r terms of the A . P . , then }S_q \text { equals }\]
If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is ____________.
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
If in an A.P., Sn = qn2 and Sm = qm2, where Sr denotes the sum of r terms of the A.P., then Sq equals ______.
