Let a 1- a 2- a 3- a 4- be an arithmetic progression and g 1- g 2- g 3- g 4- be a geometric progression- If a 1- g 1-1- a 2- g 2-4- a 3- g 3-15 and a 4- g 4-2- thenA- the common ratio of geometric progression is equal to -2-B- the common ratio of geometric progression is equal to -3C- -k-120 ak-960D- - k -120 a k -480

The correct options are B the common ratio of geometric progression is equal to –3 C ∑_k=1^20a_k = 960 Let a and d be first term and common difference of A.P. ...

Byju's Answer

Standard XII

Mathematics

Arithmetic Progression

Let a 1, a 2,...

Question

Let $a_{1}, a_{2}, a_{3}, a_{4}$ …….. be an arithmetic progression and $g_{1}, g_{2}, g_{3}, g_{4}$ …… be a geometric progression. If $a_{1} + g_{1} = 1, a_{2} + g_{2} = 4, a_{3} + g_{3} = 15 a n d a_{4} + g_{4} = 2$ , then

the common ratio of geometric progression is equal to –2.

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the common ratio of geometric progression is equal to –3

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$\sum_{k = 1}^{20} a_{k} = 960$

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$\sum_{k = 1}^{20} a_{k} = 480$

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Solution

The correct options are
B
the common ratio of geometric progression is equal to –3

C
$\sum_{k = 1}^{20} a_{k} = 960$

Let a and d be first term and common difference of A.P. Also, let b and r be the first term and common ratio of G.P.
$∴$ On solving, we get
$a = \frac{1}{2}, b = \frac{1}{2}, d = 5, r = - 3 A l s o, \sum_{k = 1}^{20} a_{k} = 960$

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