Advertisements
Advertisements
Question
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?
Advertisements
Solution
Let a be the first term and d be the common difference.
\[a_{12} = - 13\]
\[ \Rightarrow a + \left( 12 - 1 \right)d = - 13\]
\[ \Rightarrow a + 11d = - 13 . . . (i)\]
\[\text { Also, } S_4 = 24\]
\[ \Rightarrow \frac{4}{2}\left[ 2a + (4 - 1)d \right] = 24\]
\[ \Rightarrow 2\left( 2a + 3d \right) = 24\]
\[ \Rightarrow 2a + 3d = 12 . . . (ii) \]
\[\text { From (i) and (ii), we get }: \]
\[19d = - 38\]
\[ \Rightarrow d = - 2\]
\[\text { Putting the value of d in (i), we get }: \]
\[a + 11\left( - 2 \right) = - 13\]
\[ \Rightarrow a = 9\]
\[ S_{10} = \frac{10}{2}\left[ 2 \times 9 + (10 - 1)\left( - 2 \right) \right]\]
\[ \Rightarrow S_{10} = 5\left[ 18 + 9\left( - 2 \right) \right] = 0\]
APPEARS IN
RELATED QUESTIONS
Find the sum of odd integers from 1 to 2001.
Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
Let the sum of n, 2n, 3n terms of an A.P. be S1, S2 and S3, respectively, show that S3 = 3 (S2– S1)
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.
Which term of the A.P. 84, 80, 76, ... is 0?
Is 302 a term of the A.P. 3, 8, 13, ...?
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 6th and 17th terms of an A.P. are 19 and 41 respectively, find the 40th term.
If 9th term of an A.P. is zero, prove that its 29th term is double the 19th term.
The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.
Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.
Find the sum of the following arithmetic progression :
a + b, a − b, a − 3b, ... to 22 terms
Find the sum of the following arithmetic progression :
\[\frac{x - y}{x + y}, \frac{3x - 2y}{x + y}, \frac{5x - 3y}{x + y}\], ... to n terms.
Find the sum of the following serie:
2 + 5 + 8 + ... + 182
Find the sum of the following serie:
101 + 99 + 97 + ... + 47
Find the sum of all integers between 100 and 550, which are divisible by 9.
Find the sum of odd integers from 1 to 2001.
Find an A.P. in which the sum of any number of terms is always three times the squared number of these terms.
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)
If a, b, c is in A.P., prove that:
a3 + c3 + 6abc = 8b3.
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?
A man starts repaying a loan as first instalment of Rs 100 = 00. If he increases the instalments by Rs 5 every month, what amount he will pay in the 30th 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.
Write the common difference of an A.P. whose nth term is xn + y.
Write the sum of first n odd natural numbers.
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.
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
In n A.M.'s are introduced between 3 and 17 such that the ratio of the last mean to the first mean is 3 : 1, then the value of n is
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are
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 =
Mark the correct alternative in the following question:
Let Sn denote the sum of first n terms of an A.P. If S2n = 3Sn, then S3n : Sn is equal to
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of p + q terms is – (p + q). Also, find the sum of first p – q terms (p > q).
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
The sum of n terms of an AP is 3n2 + 5n. The number of term which equals 164 is ______.
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
