急 F6 Geometric Sequences 02q14

11.
T37
= (T1 + T2 + T3 + ...... + T36 + T37)- (T1 + T2 + T3 + ...... + T36)
= S37 - S36
= 37 x (37 + 1) - 36 x (36 + 1)
= 37 x 38 - 36 x 37
= 37 x (38 - 36)
= 37 x 2
= 74


12.
Let a and d be the first term and the commondifference of the arithmetic sequence respectively.

T3 + T4 = -1
(a + 2d) + (a + 3d) = -1
2a + 5d = -1 ...... [1]

S15 = 195
15 x (2a + 14d) / 2 = 195
a + 7d = 13 ...... [2]

[2]x2 - [1] :
9d = 27
d = 3

Put d = 3 into [2] :
a + 7(3) = 13
a = -8

Sum of the first 26 terms
= 26 x (2a + 25d) / 2
= 13 x [2(-8) + 25(3)]
= 767