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Byju's Answer
Standard XII
Mathematics
Summation by Sigma Method
In an AP, the...
Question
In an AP, the first term is 22, nth term is -11, and sum of first n terms is 66. Find the number of terms n and the common difference d.
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Solution
Here,
a
=
22
,
l
=
−
11
,
S
n
=
66
Therefore,
S
n
=
n
2
(
a
+
l
)
=
66
11
n
2
=
66
n
=
12
Now, last term,
l
=
a
+
(
n
−
1
)
d
=
−
11
22
+
11
d
=
−
11
d
=
−
3
Therefore, number of terms of the AP is 12 and the common difference is -3.
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In an A.P., the first term is 22, nth term is −11 and the sum to first n terms is 66. Find n and d, the common difference