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
3351	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 4 $.	2
3352	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 5 $.	2
3353	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = -5 $.	2
3354	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 12 $.	2
3355	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3356	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	2
3357	$$ a_1 = 10 ~,~ d = 1 ~,~ a_n = 1 ~,~ n = ? $$	2
3358	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3359	Find $ S_{ 66 } $ ( sum of first $ 66 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	2
3360	Find $ S_{ 65 } $ ( sum of first $ 65 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	2
3361	Find $ S_{ 55 } $ ( sum of first $ 55 $ terms ) of arithmetic progression if $ a_1 = 12000 ~~ \text{and} ~~ d = 1000 $.	2
3362	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	2
3363	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 10 $.	2
3364	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 82 ~~ \text{and} ~~ d = 9 $.	2
3365	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	2
3366	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 8 $.	2
3367	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 14 $.	2
3368	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 37 $.	2
3369	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1000 $.	2
3370	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	2
3371	$$ a_{ 3 } = 20 ~~,~~ S_{ 10 } = 500 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3372	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 12 $.	2
3373	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
3374	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
3375	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 203 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3376	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 1032 ~~ \text{and} ~~ d = 8 $.	2
3377	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 309 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
3378	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 55000 ~~ \text{and} ~~ d = 1500 $.	2
3379	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
3380	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 1100 ~~ \text{and} ~~ d = 60 $.	2
3381	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 46 ~~ \text{and} ~~ d = 8 $.	2
3382	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 46 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
3383	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 1100 ~~ \text{and} ~~ d = 100 $.	2
3384	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 673 ~~ \text{and} ~~ d = 8 $.	2
3385	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 673 ~~ \text{and} ~~ d = 8 $.	2
3386	Find $ S_{ 198 } $ ( sum of first $ 198 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = -2 $.	2
3387	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
3388	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
3389	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3390	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	2
3391	Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
3392	Find $ S_{ 49 } $ ( sum of first $ 49 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
3393	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3394	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = \left( -20 \right) $.	2
3395	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = \left( -20 \right) $.	2
3396	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 12 $.	2
3397	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	2
3398	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
3399	Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	2
3400	Find $ S_{ 72 } $ ( sum of first $ 72 $ terms ) of arithmetic progression if $ a_1 = 45 ~~ \text{and} ~~ d = 1 $.	2