If the sum of the first 14 terms of an A.P. is 1050 and the first term is 10, then find the 20th term and the $n^{ ext{th}}$ term.

Question

If the sum of the first 14 terms of an A.P. is 1050 and the first term is 10, then find the 20th term and the $n^{	ext{th}}$ term.

Accepted Answer

Step 1: $S_{14} = \frac{14}{2}(2 	imes 10 + 13d) = 1050 \Rightarrow 7(20 + 13d) = 1050$
Step 2: $20 + 13d = 150 \Rightarrow d = 10$
Step 3: $a_{20} = 10 + 19 	imes 10 = 200$
Step 4: $a_n = 10 + (n - 1) 	imes 10 = 10n$

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