the arithmetic progression : 1, 4, 7 and ..... 2, 10, 18......each contains 100 terms how many terms are common to both
Answers
13 Terms would be common in both sequence , 1, 4, 7 ..... and 2, 10, 18......each contains 100 terms
Step-by-step explanation:
1 4 7 ..................
Difference of 3
1 + 3a
Last term would be 1 + 3 * 99 = 298
2 , 10 , 18 .............
Difference of 8
2 + 8b
Last term would be 2 + 8 * 99 = 794
1 + 3a = 2 + 8b
3a = 8b + 1
=> b = 1 , a = 3
2 + 8*1 = 10
1 + 3*3 = 10
10 is the 1st common term in both
as 3 & 8 are co prime
=> After 24 this sequence will repeat
10 , 34 , 58 and so son
Last term = 10 + (n-1)24
= 24n - 14
24n - 14 ≤ 298
=> 24n ≤ 312
=> n ≤ 13
Hence 13 Terms would be common in both sequence
10 , 34 , 58 , 82 , 106 , 130 , 154 , 178 , 202 , 226 , 250 , 274 , 298
Learn More :
The 4 term of an ap is 10
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Question from some special series and AP
https://brainly.in/question/12764784
Answer:
YOUR ANSWER IS IN THE ATTACHMENT.
Step-by-step explanation:
ANSWER: 13 terms
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