Advertisements
Advertisements
Question
Find the sum of the first 51 terms of the A.P: whose second term is 2 and the fourth term is 8.
Advertisements
Solution
51 terms of an A.P whose `a_2 = 2` and `a_4 = 8`
Now
`a_2 = a + d`
2 = a + d .....(1)
Also
a_4 = a + 3d
8 = a+ 3d ....(2)
Substracting 1 from 2 we get
2d = 6
d = 3
Further substituting d = 3 in (1) we get
2 = a + 3
a = -1
Number of terms (n) = 51
First term for the given A.P. (a) = −1
So, using the formula we get,
`S_n = 51/2[2(-1) + (51 - 1)(3)]`
`= (51/2)[-2 +(50)(3)]`
`= (51/2)[-2 + 150]`
`= (51/2)[148]`
= 3774
Therefore the sum of first terms for given A.P. is 3774
APPEARS IN
RELATED QUESTIONS
How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?
If the mth term of an A.P. is 1/n and the nth term is 1/m, show that the sum of mn terms is (mn + 1)
Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.
Find the sum of all even integers between 101 and 999.
Find the sum of the first 15 terms of each of the following sequences having the nth term as
yn = 9 − 5n
The 8th term of an AP is zero. Prove that its 38th term is triple its 18th term.
Divide 24 in three parts such that they are in AP and their product is 440.
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
If the 9th term of an A.P. is zero then show that the 29th term is twice the 19th term?
There are 25 rows of seats in an auditorium. The first row is of 20 seats, the second of 22 seats, the third of 24 seats, and so on. How many chairs are there in the 21st row ?
If in an A.P. Sn = n2p and Sm = m2p, where Sr denotes the sum of r terms of the A.P., then Sp is equal to
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
Find the sum of first 1000 positive integers.
Activity :- Let 1 + 2 + 3 + ........ + 1000
Using formula for the sum of first n terms of an A.P.,
Sn = `square`
S1000 = `square/2 (1 + 1000)`
= 500 × 1001
= `square`
Therefore, Sum of the first 1000 positive integer is `square`
The sum of first five multiples of 3 is ______.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
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 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
