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18, 26, 34, 42, find the 52nd term and the explicit formula

Verified Answer :

crisforp

We have 26 - 18 = 8; 34 - 26 = 8; 42 - 34 = 8; (an arithmetic progression)
We use the formula an = a1 + (n-1)x8 (the explicit formula)
So, an = 18 + (n-1)x8 ;
Then, an = 8n + 10;
Finally, a52 =  8x52 + 10 = 426 (the 52nd term);