Question

How
the
many
terms
arithmetic sequence
there in
1, 4, 7, 10... 202​

Answer 1

hope it's helpful

it's from my Book ok ............

Answer 2

➠ AnSwer :-

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