{n^{th}} term of an A.P. is 3n - 1 .Choose from following sum of its first five terms

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8. Sequences and Series

easy

The ${n^{th}}$ term of an $A.P.$ is $3n - 1$.Choose from the following the sum of its first five terms

A

$14$

B

$35$

C

$80$

D

$40$

Solution

(d) Here ${T_n} = 3n – 1$, putting $n = 1,\;2,\;3,\;4,\;5$

we get first five terms, $2,\;5,\;8,\;11,\;14$

Hence sum is $2+5+8+11+14=40$.

Aliter : ${S_n} = \Sigma {T_n} = 3\Sigma n – \Sigma 1 = \frac{{3n(n + 1)}}{2} – n$

$ \Rightarrow $ ${S_5} = \frac{{3.5.6}}{2} – 5 = 40$.

Standard 11

Mathematics

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