The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is 167. If the sum of the first ten terms is 235, find the sum of its first twenty terms.
970
Find the
(i) sum of integers from 1 to 500 that are multiples of 2 as well as 5,
(ii) sum of integers from 1 to 500 that are multiples of 2 as well as 5 (inclusive),
(iii) sum of integers from 1 to 500 that are multiples of 2 or 5.
(i) 12750, (ii) 12750, (iii) 75250
The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. Find the 15th term.
3
An AP consists of 37 terms. The sum of the three middle-most terms is 225 and the sum of the last three is 429. Find the AP.
First term \(a=3\), common difference \(d=4\) (AP: 3, 7, 11, …)
Find the sum of integers between 100 and 200 that are
(i) divisible by 9, (ii) not divisible by 9.
(i) 1683 (ii) 13167
The ratio of the 11th term to the 18th term of an AP is \(2:3\). Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
\(a_5:a_{21}=1:3\), \(S_5:S_{21}=5:49\)
Show that the sum of an AP whose first term is \(a\), second term is \(b\) and last term is \(c\), is
\[ S = \dfrac{(a+c)(b+c-2a)}{2(b-a)}. \]
\(S=\dfrac{(a+c)(b+c-2a)}{2(b-a)}\)
Solve the equation \(-4+(-1)+2+\cdots+x=437\).
\(x=50\)
Jaspal Singh repays a loan of Rs 118000 by monthly instalments starting with Rs 1000 and increasing by Rs 100 every month. What will he pay in the 30th instalment? What amount is still unpaid after the 30th instalment?
30th instalment: Rs 3900; Unpaid after 30th: Rs 44,500
Along a straight passage, 27 flags are to be fixed at intervals of 2 m. The flags are stored at the position of the middle-most flag. Ruchi places the flags, carrying only one at a time and returning to the store each time. How much total distance does she cover to complete the job and return? What is the maximum distance she travels while carrying a flag?
Total distance: 364 m; Maximum carrying distance: 26 m