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Answers
Step-by-step explanation:
1. a3= 24
a6= 192
a+2d= 24
a+5d=192(sub)
-3d= -168
d=-168/-3
d = 56
a+2(56)= 24
a+ 112=24
a= 24-112
a= -88
a10 = a+9d
a10 = -88+9(56)
= -88+504
= 416
2. 6,12,18........(40 terms)
a= 6
d= 12-6= 6
n= 40
Sn= n/2[2a+(n-1)d]
S40= 40/2[2(6)+(40-1)6]
= 20 [12+39(6)]
= 20[12+234]
= 20(246)
= 4920
3. 5,11,17,23.........301
a= 5
d= 11 -5
= 6
an= a+(n-1)d
301= 5+(n-1)6
301= 5+6n-6
301 = 6n-1
301+1= 6n
302 = 6n
n= 302/6
n= 50.33
301 is not a term in the list of the numbers
Answer:
4). 3rd term = ar^2 = 24. & ar^5 = 192
So, just divide them,
ar^5/ar^2 = 192/24
r^3 = 8
So, r = 2
Now, 3rd term = ar^2 = 24
a = 24/4 = 6
So, 10th term = ar^9 = 6(2)^9 = 3072_____ (Ans.)
5). Sum of first 40 positive integers divisible by 6 is in AP
Where a = 6 ; d = 6 & n = 40
Sn = n/2(2a+(n-1)d)
On calculating
We get Sn = 4920______(Ans.)
6). No 301 is not the term of the given sequence.
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