Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
Find the sum of the following arithmetic progressions
`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`
Find the sum of first 20 terms of the sequence whose nth term is `a_n = An + B`
Find the value of x for which (x + 2), 2x, ()2x + 3) are three consecutive terms of an AP.
Find the sum of the following Aps:
9, 7, 5, 3 … to 14 terms
The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
Find out the sum of all natural numbers between 1 and 145 which are divisible by 4.
In an A.P., the sum of first ten terms is −150 and the sum of its next ten terms is −550. Find the A.P.
The common difference of an A.P., the sum of whose n terms is Sn, is
If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their nth terms are in the ratio
If \[\frac{5 + 9 + 13 + . . . \text{ to n terms} }{7 + 9 + 11 + . . . \text{ to (n + 1) terms}} = \frac{17}{16},\] then n =
The common difference of the A.P. is \[\frac{1}{2q}, \frac{1 - 2q}{2q}, \frac{1 - 4q}{2q}, . . .\] is
If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is
Q.5
If the numbers n - 2, 4n - 1 and 5n + 2 are in AP, then the value of n is ______.
If the nth term of an AP is (2n +1), then the sum of its first three terms is ______.
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
The sum of 40 terms of the A.P. 7 + 10 + 13 + 16 + .......... is ______.
