Find the sum of the A.P 34+32+30+___+10
Answers
Answer:
sum of the A.P i.e., the sum of 13(n) terms is 286.
Step-by-step explanation:
a(first term) = 34
d(common difference) = -2[32-34]
L(Last term) = 10
L = a+(n-1)d
10 = 34+(n-1)(-2)
10-34 = (n-1)(-2)
-24 = -2n+2
-24-2 = -2n
-26 = -2n
26 = 2n
13 = n
there are total 13 terms in the A.P
Sn = n/2[L+ a]
as n=13
S13 = 13/2 [ 10+34] => 13/2[44] => 13 * 22 = 286
so the sum of 13(n) terms is 286.
verifying(checking) :
if u want to check that my answer is correct then u can add :
34+32+30+28+26+24+22+20+18+16+14+12+10 = 286
and there are 13 terms.
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Answer: 286
Step-by-step explanation:
here we have ; a = 34 ,
d = a2 - a1
= 32 - 34
d = - 2
nth term = 10
by formula of nth term i.e, nth term = a + (n - 1) d
substituting all values we get , 10 = 34 + (n - 1) - 2
10 = 34 + -2n + 2
10 - 34 -2 = - 2n
10 - 36 = -2n
- 26 = -2n
n = -26 / -2
n = 13
now by formula to find sum of an A.P i.e, sum of n terms = n/2 [a + nth term]
substituting all values we get , sum of n terms = 13/2[34 + 10]
sum of n terms = 13/2(44)
sum of n terms = 13 *22
by solving we will get sum of n terms = 286 which is our required answer
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