20. In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
Answers
Answered by
16
Step-by-step explanation:
a+4d=30
a+11d=65
a+11d - a-4d=35
7d=35
d=5
a+20=30
a=10
s20 = n/2(2a+(n-1)d)
=20/2(20 + 95)
= 10(115)
= 1150
Answered by
12
GIVEN :
5th term of an AP = 30
a + 4d = 30 ------(1)
12th term of an AP = 65
a + 11d = 65 ------(2)
Solve eq - 1 & 2 to find Common difference (d).
a + 4d = 30
a + 11d = 65
(-)
-------------------
-7d = -35
d = 35/7
d = 5
Common Difference = 5
Now, Substitute d in eq - (1) to find first term (a)
a + 4d = 30
a + 4(5) = 30
a + 20 = 30
a = 30 - 20
a = 10
First Term = 10
In an AP sum of the terms = n/2 ( 2a + (n - 1)d
= n/2 ( 2a + (n - 1)d
= 20/2 ( 2(10) + (20 - 1)5
= 10 ( 20 + (19)5 )
= 10 ( 20 + 95)
= 10 ( 115)
= 1150
Therefore, the sum of first 20 terms = 1150.
Hope it help
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