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## If sum of 3rd and 8th terms of an A.P. is 7 and sum of 7th and 14th terms is  –3, then find the 10th term.

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Ans.    For a given A. P.;
tn = a + (n –1)d
Where a = first term
d = common difference
Sum of 3rd and 8th terms of an A.P. is 7
∴        t3 + t8 = 7
a + (3 –1)d + (a + (8 –1)d  = 7
a + 2d + a + 7d = 7
2a + 9d = 7                               ...(I)
Sum of 7th and 14th terms is –3
∴                                   t7 + t14 = –3
a + (7 – 1)d + a + (14 – 1)d = –3
a + 6d + a + 13d = –3
2a + 19d = –3                              ...(II)
Subtracting eqn. (I) From (II)

2a + 9d     =  7
–              2a + 19d   = –3
(–)    (–)          (+)

–10d =  10
d = –1
Place d = –1 in eqn. (I)
2a + 9(–1) = 7
2a – 9 = 7
2a = 7 + 9
2a = 16
a = 8
t10 = a + (10 –1)d
t10 = 8 + 9 × –1
t10 = 8 – 9 = –1
∴      The 10th them is –1

Arithmetic Progression September 28 , 2018 0 Comments 74 views