# Find the 37th term of an arithmetic sequence whose second and third terms are −4 and 12. If the fourth term of an arithmetic sequence is 17 and the second term is 3, find the 24th term.

Question
Polynomial arithmetic
Find the 37th term of an arithmetic sequence whose second and third terms are −4 and 12. If the fourth term of an arithmetic sequence is 17 and the second term is 3, find the 24th term.

2021-01-16
Step 1 Given: Second term $$(a_{2}) =\ -4$$ Third term $$(a_{3}) = 12$$ Step 2 Used concept $$T_{n} = a_{1}\ +\ (n\ -\ 1)d$$ Where $$T_{n}\ \rightarrow\ n^{(th)}\ \text{term}$$
$$a_{1}\ \rightarrow\ 1^{(st)}\ \text{term}$$
$$d\ \rightarrow\ \text{difference}\ = (a_{2}\ -\ a_{1}) = (a_{3}\ -\ a_{2})$$ Step 3 Apply the above concept it gives $$d = a_{3}\ -\ a_{2}$$
$$d = 12\ -\ (-4)$$
$$d = 12\ +\ 4 = 16$$ now, $$a_{1} = a_{2}\ -\ d$$
$$a_{1} =\ -4\ -\ 16 =\ -20$$ Step 4 The $$37^{(th)}$$ term of the given arithmetic sequence will be $$T_{37} =\ -20\ +\ (37\ -\ 1)\ \times\ 16$$
$$=\ -20\ +\ 36\ \times\ 16$$
$$=\ -20\ +\ 576$$
$$=556$$ (answer)

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