Advertisements
Advertisements
प्रश्न
If the second term and the fourth term of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:
Advertisements
उत्तर
For an A.P. t2 = 12 and t4 = 20
To find : S25 = ?
∴ tn = a+(n-1)d
∴ t2 = a+(2-1)d
∴ 12 = a + d .....eq(1)
∴ t4 = a + (4 - 1)d
∴ 20 = a + 3d ....eq(2)
Substracting eq(i) from eq(ii)
a + 3d = 20
`(a + d = 12)/(2d = 8)`
`"d" = 8/2`
∴ d = 4
Substituting d = 4 in eq (i)
a + d = 12
∴ a + 4 = 12
∴ a = 12 - 4
∴ a = 8
`"S"_"n" = "n"/2 ["2a" + ("n" - 1)"d"]`
`therefore "S"_25 = 25/2 [2(8) + (25 - 1)(4)]`
`= 25/2 [16 + 24(4)]`
`= 25/2[16 + 96]`
`= 25/2 xx 112`
= 1400
The sum of first 25 terms is 1400.
APPEARS IN
संबंधित प्रश्न
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Which term of the A.P. `20, 19 1/4, 18 1/2, 17 3/4,` ... is the first negative term?
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)
Simplify `sqrt(50)`
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 an A.P. the sum of whose n terms is Sn.
Write the sum of first n odd natural numbers.
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
If \[\frac{1}{x + 2}, \frac{1}{x + 3}, \frac{1}{x + 5}\] are in A.P. Then, x =
The common difference of the A.P. \[\frac{1}{2b}, \frac{1 - 6b}{2b}, \frac{1 - 12b}{2b}, . . .\] is
The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals
Q.13
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
Show that a1, a2, a3, … form an A.P. where an is defined as an = 3 + 4n. Also find the sum of first 15 terms.
The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
Read the following passage:
|
India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. |
- In which year, the production is 29,200 sets?
- Find the production in the 8th year.
OR
Find the production in first 3 years. - Find the difference of the production in 7th year and 4th year.
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
Which expression gives the sum of the first n natural numbers \[1 + 2 + \cdots + n\]?
