Question

If the 22nd term in the sequence is -143 and the 61st term is -416, what is the 31st term in
the sequence?

Answer 1

Step-by-step explanation:

Let a be the first term and d be the common difference of the given A.P. Then,

S

6

=42⟹

2

6

{2a+(6−1)d}=42⟹2a+5d=14 ...(i)

It is given that

a

10

:a

30

=1:3

⟹

a+29d

a+9d

=

3

1

⟹3a+27d=a+29d

⟹2a−2d=0

⟹a=d ...(ii)

putting the value of a in (i), we get

2d+5d=14⇒d=2

∴a=d=2

∴a

13

=a+12d=2+2×12=26

Hence, first term =2 and thirteenth term =26

Answer 2

Step-by-step explanation:

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