Q. 3 B4.2( 5 Votes )

# Write the next three terms of the following sequences: for all

Given: t1 = 3 and tn = 3tn-1 + 2

Now, we have to find next three terms i.e. t2, t3 and t4

Taking n = 2, we get

t2 = 3t2-1 + 2

= 3t1 + 2

= 3(3) + 2 [given: t1 = 3]

t3 = 9 + 2

t3 = 11 …(i)

Taking n = 3, we get

t3 = 3t3-1 + 2

= 3t2 + 2

= 3(11) + 2 [from (i)]

= 33 + 2

t3 = 35 …(ii)

Taking n = 4, we get

t4 = 3t4-1 + 2

= 3t3 + 2

= 3(35) +2

t5 = 105 + 2

t5 = 107 [from (ii)]

Hence, the next three terms are 11, 35 and 107.

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