If the sum of first four terms of an A.P. is 40 and that of
fourteen terms is 280, find the sum of first n terms.
(CBSE 2016)
Answers
Answer:
Brainly.in
What is your question?
Anjali2820
nikitajha400
nikitajha400
21.06.2017
Math
Secondary School
+5 pts
Answered
If the sum of first 4 terms of an AP is 40 and that of first 14 the is 280, find the sum of first n term
Answers
The Brain
Parisakura98pari Ace
Sn = sum of n terms of an A.P. = n/2 [ 2a + (n-1)d]
A/Q
S₄ = 40 = 4/2 [2a + 3d] = 2a + 3d = 20 ...........(1)
and
S₁₄ = 280 = 14/2 [2a + 13d] = 2a + 13d = 40 .........(2)
solving (1) and (2)
gives a = 7 and d= 2
so Sn = n/2[ 2(7) + (n-1)2] = 7n + n² - n = n² + 6n
I hope it helps you
plz mark me as BRAINLIEST
Answer:
Step-by-step explanation:
s4=40
s14=280
s4=4/2[2a+[4-1]d]
40/2 = [2a+3d]
20=2a+3d .......1
s14= 14/2 [2a+[14-1]d]
280=7[2a+13d]
280/7=2a+13d
40=2a+13d ........2
eq.2-eq.1
40=2a+13d
20=2a+3d
[-] [-] [-]
________
20=10d
d=2
sub. d=2 in eq.1
20=2a+3 x 2
20-6=2a
14=2a
a=7
the sum of n terms = n/2[2a+[n-1]d]
= n/2 x[14+2n-2]
= n/2 [12+2n]
n/2[2[6+n]
=n[6+n]
6n+n^2
therefore the sum of n terms is 6n+n^2