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Arithmetic Progressions
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31/05/2021 10:59 am
Topic starter
Choose the correct choice in the following and justify:
(i) 30th term of the A.P: 10,7, 4, …, is
(A) 97 (B) 77 (C) −77 (D) −87
(ii) 11th term of the A.P. -3, -1/2, ,2 …. is
(A) 28 (B) 22 (C) – 38 (D) \(-48\frac{1}{2}\)
1 Answer
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31/05/2021 11:00 am
(i) Given here,
A.P. = 10, 7, 4, …
we can find,
First term, a = 10
Common difference, d = a2 − a1 = 7−10 = −3
As we know, for an A.P.,
an = a +(n−1)d
Putting the values;
a30 = 10+(30−1)(−3)
a30 = 10+(29)(−3)
a30 = 10−87 = −77
Hence, the correct answer is option C.
(ii) Given here,
A.P. = -3, -1/2, ,2 …
Therefore, we can find,
First term a = – 3
Common difference, d = a2 − a1 = (-1/2) -(-3)
⇒(-1/2) + 3 = 5/2
As we know, for an A.P.,
an = a+(n−1)d
Putting the values;
a11 = 3+(11-1)(5/2)
a11 = 3+(10)(5/2)
a11 = -3+25
a11 = 22
Hence, the answer is option B.