Advertisements
Advertisements
Question
Find the sum given below:
34 + 32 + 30 + ... + 10
Advertisements
Solution
34 + 32 + 30 + ... + 10
For this A.P.,
a = 34
d = a2 − a1
= 32 − 34
= −2
l = 10
Let 10 be the nth term of this A.P.
l = a + (n − 1) d
10 = 34 + (n − 1) (−2)
−24 = (n − 1) (−2)
12 = n − 1
n = 13
Sn = `n/2(a+1)`
= `13/2(34+10)`
= `(13xx44)/2`
= 13 × 22
= 286
APPEARS IN
RELATED QUESTIONS
Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
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)
Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....
Find how many integers between 200 and 500 are divisible by 8.
If (m + 1)th term of an A.P is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Find the sum of all odd numbers between 100 and 200.
Find the sum of the first 22 terms of the A.P. : 8, 3, –2, ………
Which term of the AP 21, 18, 15, …… is -81?
Find the 25th term of the AP \[- 5, \frac{- 5}{2}, 0, \frac{5}{2}, . . .\]
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
Find the sum of all 2 - digit natural numbers divisible by 4.
Write the common difference of an A.P. whose nth term is an = 3n + 7.
Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.
If the sum of n terms of an A.P. is 3n2 + 5n then which of its terms is 164?
If the sum of n terms of an A.P. is 2n2 + 5n, then its nth term is
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
Sum of n terms of the series `sqrt2+sqrt8+sqrt18+sqrt32+....` is ______.
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
Find the sum of first 10 terms of the A.P.
4 + 6 + 8 + .............
Find the value of x, when in the A.P. given below 2 + 6 + 10 + ... + x = 1800.
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
In an A.P. (with usual notations) : given d = 5, S9 = 75, find a and a9
In a ‘Mahila Bachat Gat’, Sharvari invested ₹ 2 on first day, ₹ 4 on second day and ₹ 6 on third day. If she saves like this, then what would be her total savings in the month of February 2010?
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment
Find the sum:
1 + (–2) + (–5) + (–8) + ... + (–236)
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
Find the sum of all odd numbers between 351 and 373.
Sum of 1 to n natural number is 45, then find the value of n.
