Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

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ID	Problem	Count
101	$$ a_1 = 16 ~,~ a_n = 163 ~,~ S_n = 4475 ~,~ n = ? $$	12
102	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	12
103	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -5 \right) $.	12
104	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	12
105	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 8 $.	12
106	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	12
107	Find $ a_{ 59 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = \left( -9 \right) $.	12
108	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	12
109	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 4 $.	12
110	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 16 $.	12
111	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	12
112	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	11
113	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	11
114	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	11
115	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 250000 ~~ \text{and} ~~ d = 25000 $.	11
116	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	11
117	$$ a_1 = 3 ~,~ d = 5 ~,~ a_n = 183 ~,~ n = ? $$	11
118	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	11
119	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	11
120	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	11
121	Find $ S_{ 333 } $ ( sum of first $ 333 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	11
122	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -3 \right) $.	11
123	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $.	11
124	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	11
125	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	11
126	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	11
127	$$ a_1 = 19 ~,~ a_n = 96 ~,~ S_n = 690 ~,~ n = ? $$	11
128	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	11
129	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	11
130	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $.	11
131	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $.	11
132	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	11
133	Find common difference $ d $ of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 5 } = 18 $.	11
134	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ S_{ 10 } = 145 $.	11
135	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -27 ~~ \text{and} ~~ d = 3 $.	11
136	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 8 $.	11
137	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	11
138	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	11
139	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	11
140	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 2 }{ 5 } $.	11
141	Find $ a_{ 75 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 16 $.	11
142	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 0 $.	11
143	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	11
144	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	11
145	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	11
146	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	11
147	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	11
148	Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	11
149	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	11
150	Find $ a_{ 63 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 6 $.	11