We have been given that the sum of first six terms of an AP is 42. The ratio of its 10th term to 30th term is 1:3 find the first and 13th term of an AP.
ML Aggarwal
Avichal Publication
Arithmetic Progression
Chapter 9 Question no 15
Rajan@2021Guru
Sum of first six terms of an AP is 42. The ratio of its 10th term to 30th term is 1:3 find the first and 13th term of an AP.
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Sum of the first n terms is given by
Sn=2n[2a+(n−1)d]
S6=26[2a+(6−1)d]
S6=3[2a+5d]
T30T10=31
a+29da+9d=31
(a+9d)3=(a+29d)1
3a+27d=a+29d
2a=2d
a=d…(1)
S6=3[2a+5d]
S6=3[2a+5a]
42=3(7a)
42=21a
∴a=2
From (1)
d=a=2
T13=a+(n−1)d
=2+(13−1)2
=2+24
=26