Arithmetic sequences

(the database of solved problems)

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

Select category

ID	Problem	Count
3301	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3302	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	2
3303	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 0 $.	2
3304	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 2 $.	2
3305	$$ a_1 = 25 ~,~ d = 3 ~,~ S_n = 47 ~,~ n = ? $$	2
3306	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3307	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 500 $.	2
3308	Find $ a_{ 165 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
3309	Find $ S_{ 73 } $ ( sum of first $ 73 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 9 $.	2
3310	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -3 $.	2
3311	$$ a_{ 3 } = 12 ~~,~~ S_{ 6 } = 42 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3312	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 94 ~~ \text{and} ~~ d = \left( -19 \right) $.	2
3313	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 94 ~~ \text{and} ~~ d = \left( -\frac{ 37 }{ 2 } \right) $.	2
3314	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 94 ~~ \text{and} ~~ d = \left( -\frac{ 93 }{ 5 } \right) $.	2
3315	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 94 ~~ \text{and} ~~ d = \left( -29 \right) $.	2
3316	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 94 ~~ \text{and} ~~ d = \left( -30 \right) $.	2
3317	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 94 ~~ \text{and} ~~ d = 1 $.	2
3318	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 3 $.	2
3319	Find $ a_{ 333 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
3320	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -17 $.	2
3321	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 9 $.	2
3322	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3323	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 10 $.	2
3324	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = -24 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
3325	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 7 $.	2
3326	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 7 $.	2
3327	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3328	Find $ a_{ 99 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3329	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3330	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 159 ~~ \text{and} ~~ d = -14 $.	2
3331	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3332	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3333	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 3 $.	2
3334	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
3335	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 504 ~~ \text{and} ~~ d = 5 $.	2
3336	Find $ a_{ 333 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 5 $.	2
3337	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 59 }{ 50 } ~~ \text{and} ~~ d = \frac{ 2 }{ 25 } $.	2
3338	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = \frac{ 59 }{ 50 } ~~ \text{and} ~~ d = \frac{ 2 }{ 25 } $.	2
3339	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $.	2
3340	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = -\frac{ 5 }{ 2 } $.	2
3341	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3342	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = \frac{ 15 }{ 2 } ~~ \text{and} ~~ d = \frac{ 13 }{ 2 } $.	2
3343	$$ a_{ 5 } = -9 ~~,~~ S_{ 8 } = -18 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3344	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = 0 $.	2
3345	Find $ a_{ 85 } $ of an arithmetic progression if $ a_1 = 87 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3346	Find $ a_{ 95 } $ of an arithmetic progression if $ a_1 = 87 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3347	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 4 $.	2
3348	Find $ a_{ 303 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
3349	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
3350	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 6 $.	2