Advertisements
Advertisements
Question
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
Advertisements
Solution
For an A.P.
t8 = 37
`=>` a + 7d = 37 ...(i)
Also, t15 – t12 = 15
`=>` (a + 14d) – (a + 11d) = 15
`=>` a + 14d – a – 11d = 15
`=>` 3d = 15
`=>` d = 5
Substituting d = 5 in (i), we get
a + 7 × 5 = 37
`=>` a + 35 = 37
`=>` a = 2
∴ Required A.P. = a, a + d, a + 2d, a + 3d, .....
= 2, 7, 12, 17, .....
Sum of the first 20 terms of this A.P.
= `20/2 [2 xx 2 + 19 xx 5]`
= 10[4 + 95]
= 10 × 99
= 990
APPEARS IN
RELATED QUESTIONS
If Sn1 denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.
What value is generated in the above situation?
Find the sum of the following arithmetic progressions:
1, 3, 5, 7, ... to 12 terms
Find the sum of the first n natural numbers.
Find the first term and common difference for the A.P.
0.6, 0.9, 1.2,1.5,...
If the sum of first p terms of an A.P. is equal to the sum of first q terms then show that the sum of its first (p + q) terms is zero. (p ≠ q)
The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
The sum of first 16 terms of the AP: 10, 6, 2,... is ______.
The sum of all two digit numbers is ______.
