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Number of identical terms in the sequence 2, 5, 8, 11,___ upto

Question

Number of identical terms in the sequence $2, 5, 8, 11,$ _ upto $100$ terms and $3, 5, 7, 9, 11$ __ upto $100$ terms are

17

33

50

147

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Number of identical terms in the sequence

2, 5, 8, 11,

___ upto

100

terms and

3, 5, 7, 9, 11

____ upto

100

terms are

14 mins ago

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14 mins ago

Text solutionVerified

Fierst series:

2, 5, 8, 11.........

a_{1} = 2; d = 3; n = 100

l = 20 (100 - 1)^{*} 5 = 2 + 9 9^{*} 3 = 2 + 297 = 299

so, series

= 2, 5, 8, 11, ....., 197, 197, 200, 203, ...., 299

second series;

3, 5, 9, 11, .....

a_{1} = 3; d = 2; n = 100

l = 3 + (100 - 1)^{*} 2 = 3 + 9 9^{*} 2 = 3 + 198 = 201

so series

= 3, 5, 7, 9, 11, ...., 201

series having similar terms;

5, 11, 17, ....., 197

a_{1} = 5; d = 6; l = 197

l = a_{1} + (n - 1) d

197 = 5 + (n - 1) 6

192/6 = n - 1

32 + 1 = n

n = 33

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Question Text	Number of identical terms in the sequence $2, 5, 8, 11,$ ___ upto $100$ terms and $3, 5, 7, 9, 11$ ____ upto $100$ terms are
Answer Type	Text solution:1
Upvotes	150