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
If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.
In an AP Given a12 = 37, d = 3, find a and S12.
In an AP given d = 5, S9 = 75, find a and a9.
Choose the correct alternative answer for the following question .
If for any A.P. d = 5 then t18 – t13 = ....
In an A.P. the first term is – 5 and the last term is 45. If the sum of all numbers in the A.P. is 120, then how many terms are there? What is the common difference?
Find the sum of all 2-digit natural numbers divisible by 4.
The sum of first n terms of an A.P. is 5n − n2. Find the nth term of this A.P.
The sum of first n terms of an A.P is 5n2 + 3n. If its mth term is 168, find the value of m. Also, find the 20th term of this A.P.
If the sum of first n terms of an A.P. is \[\frac{1}{2}\] (3n2 + 7n), then find its nth term. Hence write its 20th term.
Write the common difference of an A.P. whose nth term is an = 3n + 7.
Write the sum of first n odd natural numbers.
Sum of n terms of the series `sqrt2+sqrt8+sqrt18+sqrt32+....` is ______.
If 18, a, b, −3 are in A.P., the a + b =
An article can be bought by paying Rs. 28,000 at once or by making 12 monthly installments. If the first installment paid is Rs. 3,000 and every other installment is Rs. 100 less than the previous one, find:
- amount of installments paid in the 9th month.
- total amount paid in the installment scheme.
Q.10
If an = 3 – 4n, show that a1, a2, a3,... form an AP. Also find S20.
Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
Sum of 1 to n natural number is 45, then find the value of n.
The sum of n terms of an A.P. is 3n2. The second term of this A.P. is ______.
