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Common Difference

a T n = n fin...

Question

(a) T_n = n find (i) T_n+1 (ii) T _n−1

(b) If T_n = n² − 1 find (i) T_n−2 (ii) T_n+1

(c) If T_n = 2n² + 1 find the value of n if T_n = 73

(d) In a sequence T_n= 5 − 3n find (i) T_n+1 (ii) T_n+2

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Solution

(a)

(i) To find , substitute n + 1 in place of n in.

(ii) To find , substitute n − 1 in place of n in.

(b)

(i) To find , substitute n − 2 in place of n in.

(ii) To find, substitute n + 1 in place of n in.

(c)

It is given that .

Since n is a natural number, n = 6.

(d)

(i) To find, substitute n + 1 in place of n in.

(ii) To find, substitute n + 2 in place of n in.

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Similar questions

If $T_{n} = n^{2} - 1$ , find (i) $T_{n - 1}$ (ii) $T_{n + 1}$

T_{1} = T_{2} = 1

T_{1}, T_{2}, T_{3}, . . ., T_{n}

is a sequence and

T_{n + 2} = (T_{n + 1})^{- 1} + T_{n}

n = 1, 2, 3

T_{2019}

.

Q. Assertion :If the sequence

{t_{n}}

is monotonically increasing ihen the sequence

{\sum t_{n}},

\sum t_{n} = \frac{t_{1} + t_{2} + . . . + t_{n}}{n}

is also monotonically increasing Reason: If

{t_{n}}

is monotonically increasing then the expression

\sum t_{n + 1} - \sum t_{n}

Q. Assertion :If

S_{n} =^{n} C_{1} - \frac{^{n} C_{2}}{2} + \frac{^{n} C_{3}}{3} - . . . . . + \frac{{(- 1)}^{n - 1}^{n} c_{n}}{n}

T_{n} = 1 + \frac{1}{2} + \frac{1}{3} + . . . + \frac{1}{n}

S_{n} = T_{n} \forall n

S_{n + 1} - S_{n} = T_{n + 1} - T_{n}

T_{n} = n^{2} + 4

T_{n} = 200

, find the value of

n

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