374.
Z a1=2; an=2n; Sn= (a1 + an )n = (2 + 2n)n = 2n(n + 1) = (n + 1)n . [
2 2 2 (1 + 2n − 1) ⋅ n 2n ⋅ n 2 = =n . a1=1; an=2n–1; Sn= 2 2
375.
Z a1=1; a150=150; n=150; S150= (150 + 1) ⋅150 = 11325 . 2 [ ≤n≤120; a1=20; a101=120; n=101 (a1 + a101 ) ⋅101 (20 + 120) ⋅101 = = 7070 . 2 2 \ an=4n; 4n≤300; n≤75; a1=4; a75=4 (4 + 300) ⋅ 75 = 11400 . S75= 2 S101=
Â
] an=7n; 7n≤130; n≤ ; n=18; a1=7; a18=7Â
S18=
(7 + 126) â‹…18 = 1197. 2
376. a1=10; d=3; a n=a1+d(n–1); a15=10+3(15–1)=52; a30=10+3(30–1)=97; (a + a n )n (a + a 30 )16 (52 + 97)16 = = 1192. ; S= 15 Sn= 1 2 2 2
377. a1=21; d=–0,5; an=a1+d(n–1); a6=21–0,5(6–1)=18,5; a25=21–0,5(25–1)=9; (a + a n ) ⋅ n ( a + a 25 ) ⋅ 20 (18,5 + 9) ⋅ 20 Sn= 1 = = 275. ; S= 6 2 2 2
378. 1) cn=c1+d(n1); c1 + 6d = 18,5,  c1 + 16d = −26,5;
10d = −45, d = −4,5, d = −4,5,    + = 6 18 , 5 ; c d = − ⋅ − 18 , 5 6 ( 4 , 5 ); c  1 1 c1 = 45,5. 2c + d (n − 1) 2 ⋅ 45,5 − 4,5( 20 − 1) 2) Sn= 1 ⋅ n; S20= ⋅ 20 = 55. 2 2
3
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