Consider a series whose sum to n-terms is denoted by Sn - nth term is tn where Sn-n3-2n-1 - n - N- then the value of t5-t3 is equal to

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Differentiation to Solve Modified Sum of Binomial Coefficients

Consider a se...

Question

Consider a series whose sum to n-terms is denoted by $S_{n} & n^{t h}$ term is $t_{n}$ where $S_{n} = n^{3} + 2^{n + 1} \forall n \in N$ , then the value of $(t_{5} - t_{3})$ is equal to

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Solution

The correct option is A $12$
$S_{n} = n^{3} + 2^{n + 1} S_{1} = 1 + 2^{3} + 2^{2} = 5 = t_{1} = a S_{2} = 2^{3} + 2^{2 + 1} = 8 + 8 = 16 \Rightarrow t_{1} + t_{2} = 16 \Rightarrow t_{2} = 11 \Rightarrow a + d = 11 \Rightarrow d = 6 ∴ t_{3} = \infty + 2 d = 5 + 2 \times 6 = 17 t_{5} = a + 4 d = 5 + 4 \times 6 = 29 ∴ t_{5} - t_{3} = 29 - 17 = 12$

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Similar questions

Q. If the

n^{t h}

term of the series is

T_{n} = 2 n - 1

, then sum of

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S_{n}

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Q. If the

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2, 12, 36, 80, 150, 252, . . . . .

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S_{n} = a_{1} + a_{2} + . . . + a_{n}

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S_{n - 1} = a_{1} + a_{2} + . . . + a_{n - 1} (\forall n > 1)

and then we can write

t_{n} = S_{n} - S_{n - 1} \forall n \geq 2

for

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On the basis of above information answer the following questionsThe sum to

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Consider a series whose sum to n-terms is denoted by Sn&nth term is tn where Sn=n3+2n+1∀n∈N, then the value of (t5−t3) is equal to

The correct option is A 12Sn=n3+2n+1S1=1+23+22=5=t1=aS2=23+22+1=8+8=16⇒t1+t2=16⇒t2=11⇒a+d=11⇒d=6∴t3=∞+2d=5+2×6=17t5=a+4d=5+4×6=29∴t5−t3=29−17=12

Consider a series whose sum to n-terms is denoted by $S_{n} & n^{t h}$ term is $t_{n}$ where $S_{n} = n^{3} + 2^{n + 1} \forall n \in N$ , then the value of $(t_{5} - t_{3})$ is equal to