1. a) The term of an Arithmetic Progression is 3n+8. Determine which term in A.P is equal to 101. b) The first term of an A.P is 11. The sum of the first six terms is 96 and the sum of the entire series is 200. Determine the common difference and the number of terms. [ 8 marks ]
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Step-by-step explanation:
Here a=100
Let difference is d.
⇒a
1
+a
2
+a
3
+a
4
+a
5
+a
6
=5(a
7
+a
8
+a
9
+a
10
+a
11
+a
12
)
So by the formula, S
n
=
2
n
(a+l), where a &l are the first and last term of an AP, we have
6(
2
a
1
+a
6
)=5×6(
2
a
7
+a
12
)
⇒a
1
+a
6
=5(a
7
+a
12
)
⇒a+a+5d=5(a+6d+a+11d)
⇒2a+5d=10a+85d
⇒80d=−8a
⇒d=
10
−a
⇒
10
−100
⇒−10
Solve any question of Arithmetic Progression with:-
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