Consider two A.P.: `S_2:2,7,12 ,17 , 500 terms` `a n dS_1:1,8,15 ,22 , 300 terms` Find the number of common term. Also find the last common term.

Explanation

`S_(1):2,7,12,17,…500` terms
`rArrT_(500)=2+(500-1)5=2497`
`S_(2),1,8,15,22,…300` terms
`rArrT_(300)`=1+(300-1)7=2094
Common difference of `S_(1)` and `S_(2)` are 5 and 7, respectively.
Hence, common difference of common term series is 35 (LCM of 5 and 7)
So, A.P. of common terms is 22,57,92,...
Let last term be 2094 `rArr`22+(n-1)35=2094`rArr`n=60.2
But n is natural number `rArr`n=60
Then actual last common term = 22 +(60-1)35=2087