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.
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
How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?
Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 − 3n.
In an A.P. the first term is 25, nth term is –17 and the sum of n terms is 132. Find n and the common difference.
The 7th term of the an AP is -4 and its 13th term is -16. Find the AP.
The sum of three numbers in AP is 3 and their product is -35. Find the numbers.
Find the first term and common difference for the A.P.
`1/4,3/4,5/4,7/4,...`
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
If the first term of an A.P. is 5, the last term is 15 and the sum of first n terms is 30, then find the value of n.
Find the sum of first 16 terms of the A.P. whose nth term is given by an = 5n – 3.
Three numbers in A.P. have the sum of 30. What is its middle term?
