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
351	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -3 \right) $.	7
352	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -4 \right) $.	7
353	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -3 \right) $.	7
354	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	7
355	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 47 ~~ \text{and} ~~ d = \left( -5 \right) $.	7
356	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	7
357	Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	7
358	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 41 ~~ \text{and} ~~ d = -4 $.	7
359	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	7
360	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 12 } = 35 $.	7
361	Find $ a_{ 98 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 2 $.	7
362	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 319 }{ 100 } ~~ \text{and} ~~ d = \frac{ 28 }{ 25 } $.	7
363	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	7
364	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	7
365	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 2 $.	7
366	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 6 $.	7
367	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $.	7
368	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 9 $.	7
369	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 2 $.	7
370	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 3 }{ 8 } $.	7
371	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 3 }{ 8 } $.	7
372	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 5 $.	7
373	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = -5 $.	7
374	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -3 \right) $.	7
375	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	7
376	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	7
377	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 15 $.	7
378	Find $ a_{ 66 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 17 $.	7
379	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	7
380	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	7
381	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	7
382	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $.	7
383	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 10 $.	7
384	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	7
385	Find $ S_{ 89 } $ ( sum of first $ 89 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	7
386	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -4 $.	7
387	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	7
388	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 0 $.	7
389	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 5 $.	7
390	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	7
391	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	7
392	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	7
393	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	7
394	$$ a_1 = -2 ~,~ d = -10 ~,~ S_n = -224 ~,~ n = ? $$	7
395	$$ a_1 = -3 ~,~ d = 2 ~,~ S_n = 21 ~,~ n = ? $$	7
396	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	7
397	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	7
398	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -\frac{ 5 }{ 4 } ~~ \text{and} ~~ d = 1 $.	7
399	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	7
400	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 8 } = 50 $.	7