Find the sum of the following arithmetic progressions:
(i)50,46,42,...to 10 terms
(ii)1,3,5,7,...to 12 terms
(iii)3,9/2,6,15/2,...to 25 terms
(iv)41,36,31,...to 12 terms
(v)a+b,a-b,a-3b,...to 22 terms
(vi)(x-y)²,(x²+y²),(x+y)²,...,to n terms
(vii)x-y/x+y,3x-2y/x+y,5x-3y/x+y,...to n terms
(viii)-26,-24,-22,...to 36 terms
Answers
Sum = 320 for AP 50,46,42,...to 10 terms
Step-by-step explanation:
Sum of n term of an AP is given by
S = (n/2)(2a + (n-1)d)
a = First Term
n = number of Terms
d = Common Difference
(i)50,46,42,...to 10 terms
a = 50
d = - 4 ( 46 - 50 = - 4)
n = 10
S = (10/2)(2*50 + (10 - 1)(-4))
= 5(100 - 36)
= 5 * 64
= 320
(ii)1,3,5,7,...to 12 terms
a = 1
d = 2 ( 3 - 1 = 2)
n = 12
S = (12/2)(2*1 + (12 - 1) * 2)
= 6 ( 2 + 22)
= 144
Do all others same way
or post Questions one by one
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Step-by-step explanation:
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