Advertisements
Advertisements
प्रश्न
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.
उत्तर
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
संबंधित प्रश्न
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Find the sum of all odd natural numbers less than 50.
What is the sum of first 10 terms of the A. P. 15,10,5,........?
The sum of third and seventh term of an A. P. is 6 and their product is 8. Find the first term and the common difference of the A. P.
Write the nth term of the \[A . P . \frac{1}{m}, \frac{1 + m}{m}, \frac{1 + 2m}{m}, . . . .\]
Sum of n terms of the series `sqrt2+sqrt8+sqrt18+sqrt32+....` is ______.
Q.3
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?
Sum of 1 to n natural number is 45, then find the value of n.
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 – n)..
Find:
- its first term and common difference
- sum of its first 25 terms
