Arithmetic Progression Extra Hots Sums for practice with answer.

In an arithmetic series, the sum of first 14 terms is -203 and the sum of the next 11 terms is –572. Find the arithmetic series.

Three numbers are in the ratio 2 : 5 : 7. If 7 is subtracted from the second, the resulting numbers form an arithmetic sequence. Determine the numbers.

If a person joins his work in 2010 with an annual salary of Rs.30,000 and receives an annual increment of `Rs. 600 every year, in which year, will his annual salary be `Rs. 39,000?

In a flower garden, there are 23 rose plants in the first row, 21 in the second row, 19 in the third row and so on. There are 5 rose plants in the last row. How many rows are there in the flower garden?

Find the smallest positive integer n such that tn of the arithmetic sequence 20, 19 1/4, 18 1/2, .... is negative?

Find the first term 'a' and the common difference 'd'

Find the first term 'a' and the common difference 'd'.

Is the sequence is an A.P. ?

Is the sequence is an A.P?


Try your self. 

1. The first term of an A.P. is 6 and the common difference is 5. Find the A.P. and its general term. (Ans. A.P. : 6, 11, 16, .... and General Term t_n = 5n + 1)

2. Find the common difference and 15th term of the A.P. 125, 120, 115, 110,.... (Ans. Common difference is d = -5 , t₁₅ = 55)

3. Find the 12th term of the A.P. 2, 3 √2, 5 √2 ....... (Ans. 12^th term t₁₂ = 23√2 )

4. Find the 17th term of the A.P. 4, 9, 14, .....  (Ans. 17^th term t­₁₇ = 84)

5. How many terms are there in the following Arithmetic Progressions? 7, 13, 19,............. , 205.  (Ans. 34 terms)

6. If 9th term of an A.P. is zero, prove that its 29th term is double (twice) the 19th term.

7. The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find the 27th term.  (Ans. t₂₇ = 109)

8. Find n so that the nth terms of the following two A.P.’s are the same.

1, 7, 13, 19, and 100, 95, 90, ....... (n = 10)

9. How many two digit numbers are divisible by 13? (Ans. 7)

10. A TV manufacturer has produced 1000 TVs in the seventh year and 1450 TVs in the tenth year. Assuming that the production increases uniformly by a fixed number every year, find the number of TVs produced in the first year and in the 15th year. (Ans. t₁  = 100, t₁₅  = 2200)

11. A man has saved Rs. 640 during the first month, Rs. 720 in the second month and Rs. 800 in the third month. If he continues his savings in this sequence, what will be his savings in the 25th month? (Ans. 2560)

12. The sum of three consecutive terms in an A.P. is 6 and their product is 120. Find the three numbers. (Ans. 10, 2 , -6  or -6 , 2 , 10)

14. Find the three consecutive terms in an A. P. whose sum is 18 and the sum of their squares is 140. (Ans. 2 , 6 , 10 or 10 , 6, 2)

15. If m times the mth term of an A.P. is equal to n times its nth term, then show that the (m+n)th term of the A.P. is zero.