Advertisements
Advertisements
Question
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
Advertisements
Solution
It is given that,
t9 = 0
Now,
tn = a + (n - 1)d
t9 = a + (9 - 1)d
⇒ 0 = a + 8d
⇒ a = -8d ...(1)
t29 = a + (29 - 1)d
= -8d + 28d
= 20d ...(2)
t19 = a + (19 - 1)d
= -8d + 18d
= 10d ...(3)
From (2) and (3), we get
t29 = 2t19
Hence, the 29th term is twice the 19th term.
APPEARS IN
RELATED QUESTIONS
If the mth term of an A.P. is 1/n and the nth term is 1/m, show that the sum of mn terms is (mn + 1)
Find the sum given below:
`7 + 10 1/2 + 14 + ... + 84`
The first and last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
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 all integers between 100 and 550, which are divisible by 9.
Find the three numbers in AP whose sum is 15 and product is 80.
The fourth term of an A.P. is 11. The sum of the fifth and seventh terms of the A.P. is 34. Find its common difference.
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
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 \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].
Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .
Mark the correct alternative in each of the following:
If 7th and 13th terms of an A.P. be 34 and 64 respectively, then its 18th term is
The 9th term of an A.P. is 449 and 449th term is 9. The term which is equal to zero is
Q.18
How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?
Find S10 if a = 6 and d = 3.
Shubhankar invested in a national savings certificate scheme. In the first year he invested ₹ 500, in the second year ₹ 700, in the third year ₹ 900 and so on. Find the total amount that he invested in 12 years.
The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
