Advertisements
Advertisements
Question
Find the sum of the following APs.
−37, −33, −29, …, to 12 terms.
Solution
−37, −33, −29, …, to 12 terms
For this A.P.,
a = −37
d = a2 − a1
= (−33) − (−37)
= −33 + 37
= 4
n = 12
We know that,
Sn = `n/2 [2a+(n - 1) d]`
S12 = `12/2 [2(-37)+(12 - 1) × 4]`
= 6[-74 + 11 × 4]
= 6[-74 + 44]
= 6(-30)
= -180
Thus, the sum of first 12 terms is -180.
RELATED QUESTIONS
In an AP, given a = 7, a13 = 35, find d and S13.
Find the sum of first 40 positive integers divisible by 6.
A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
Find the sum of the following arithmetic progressions:
41, 36, 31, ... to 12 terms
Find the sum of the first 15 terms of each of the following sequences having the nth term as
`a_n = 3 + 4n`
Find the sum of the first 15 terms of each of the following sequences having the nth term as
bn = 5 + 2n
In an A.P. the first term is 25, nth term is –17 and the sum of n terms is 132. Find n and the common difference.
Find the sum of all multiples of 7 lying between 300 and 700.
Write the next term for the AP` sqrt( 8), sqrt(18), sqrt(32),.........`
If (2p +1), 13, (5p -3) are in AP, find the value of p.
If the sum of first n terms is (3n2 + 5n), find its common difference.
The sum of the first n terms in an AP is `( (3"n"^2)/2 +(5"n")/2)`. Find the nth term and the 25th term.
The A.P. in which 4th term is –15 and 9th term is –30. Find the sum of the first 10 numbers.
If first term of an A.P. is a, second term is b and last term is c, then show that sum of all terms is \[\frac{\left( a + c \right) \left( b + c - 2a \right)}{2\left( b - a \right)}\].
The sum of first n terms of an A.P. is 3n2 + 4n. Find the 25th term of this A.P.
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
The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
The 5th term and the 9th term of an Arithmetic Progression are 4 and – 12 respectively.
Find:
- the first term
- common difference
- sum of 16 terms of the AP.
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.
