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
3251	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 194 ~~ \text{and} ~~ d = 7 $.	2
3252	$$ a_1 = 194 ~~,~~ d = 7 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3253	$$ a_1 = \frac{ 293 }{ 5 } ~,~ d = \frac{ 23 }{ 10 } ~,~ a_n = 11 ~,~ n = ? $$	2
3254	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	2
3255	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 0 $.	2
3256	Find $ a_{ 401 } $ of an arithmetic progression if $ a_1 = -24 ~~ \text{and} ~~ d = 5 $.	2
3257	$$ a_1 = 1 ~,~ d = \frac{ 1 }{ 4 } ~,~ a_n = 20 ~,~ n = ? $$	2
3258	$$ a_1 = -7 ~,~ d = 2 ~,~ S_n = 105 ~,~ n = ? $$	2
3259	Find $ S_{ 5000 } $ ( sum of first $ 5000 $ terms ) of arithmetic progression if $ a_1 = 200000 ~~ \text{and} ~~ d = 10 $.	2
3260	Find $ a_{ 111 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 100 $.	2
3261	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = \frac{ 17 }{ 20 } $.	2
3262	Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = -1352 ~~ \text{and} ~~ d = 18 $.	2
3263	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3264	Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3265	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	2
3266	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 11 $.	2
3267	Find $ a_{ 53 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 51 }{ 10 } $.	2
3268	Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
3269	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
3270	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
3271	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
3272	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 2 $.	2
3273	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 68 ~~ \text{and} ~~ d = -12 $.	2
3274	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 1 $.	2
3275	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	2
3276	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 15 $.	2
3277	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 2 $.	2
3278	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 3 }{ 10 } $.	2
3279	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -15 \right) $.	2
3280	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3281	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 5 $.	2
3282	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3283	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 10 $.	2
3284	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 4 $.	2
3285	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 0 $.	2
3286	$$ a_1 = 35 ~,~ d = 3 ~,~ a_n = 1976 ~,~ n = ? $$	2
3287	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
3288	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = \frac{ 948 }{ 5 } ~~ \text{and} ~~ d = \left( -\frac{ 173 }{ 10 } \right) $.	2
3289	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $.	2
3290	Find $ a_{ 129 } $ of an arithmetic progression if $ a_1 = \frac{ 9 }{ 5 } ~~ \text{and} ~~ d = \left( -\frac{ 13 }{ 5 } \right) $.	2
3291	Find $ a_{ 150 } $ of an arithmetic progression if $ a_1 = -\frac{ 47 }{ 10 } ~~ \text{and} ~~ d = \frac{ 23 }{ 10 } $.	2
3292	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 2 $.	2
3293	$$ a_1 = 39 ~,~ d = 7 ~,~ a_n = 4 ~,~ n = ? $$	2
3294	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = \frac{ 13 }{ 5 } $.	2
3295	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 0 $.	2
3296	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	2
3297	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = -2 $.	2
3298	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
3299	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = \left( -20 \right) $.	2
3300	Find $ S_{ 298 } $ ( sum of first $ 298 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	2