Progressions & Series Test -1

Result

Progressions & Series Test -1

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

The sum of n terms of an AP is 3n² + 5n. The position of the term which equals 164 is-

A
13

B
21

C
27

D
None of these

Solution

S_n = 3n² + 5n
T_n = S_n – S_n–1
= 3n² + 5n – [3 (n – 1)² + 5 (n – 1)] = 164 given
⇒ 6n + 2 = 164
⇒ n = 27
Question 2
1 / -0

If a, b, c, d are in G.P. then a + b, b + c, c + d are in-
A.

A
P.

B
G.P.

C
H.P.

D
None of these

Solution

∵ a, b, c, d are in G.P.
⇒ ad = bc and b² = ac and c² = bd
⇒ b² + c² = ac + bd
⇒ (b + c)² = ac + bd + 2bc
⇒ (b + c)² = ac + bd + bc + ad [∵ ad = bc]
⇒ (b + c)² = (a + b) (c + d)
⇒ (a + b), (b + c), (c + d) are in G.P.