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Common Difference

If tn represe...

Question

If $t_{n}$ represents $n^{t h}$ term of an A. P., $t_{2} + t_{5} - t_{3} = 10$ and $t_{2} + t_{9} = 17$ , find its first term and its common difference.

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Solution

given

, t2+t5−t3=10 and t2+t9=17
using tn=a+(n-1)d
t2+t5−t3=10, can be written as a +3d=10 which can also be written as 2a+6d=20......................(1)
simmilarly
t2+t9=17,can be written as 2a+9d=17.......................(2)
subtracting both equations

3d=-3
d=-1=common difference

so
a=13=first term

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t_{n}

n^{t h}

term of an A.P.,

t_{2} + t_{5} - t_{3} = 10

t_{2} + t_{9} = 17

, then find its first term and its common difference.

t_{n} = n (n + 3)

, then find the difference of its

5^{t h}

2^{n d}

t_{5} - t_{2}

T_{0}, T_{1}, T_{2}, . . . . . T_{n}

represent the term in the expansion of

(x + a)^{n}

, then the value of

(T_{0} - T_{2} + T_{4} - T_{6} + . . . . .)^{2} + (T_{1} - T_{3} + T_{5} + . . . . .)^{2}

T_{0}, T_{1}, T_{2}, . . ., T_{n}

represent in the terms in the expansion of

{(x + a)}^{n}

, then the value of

{(T_{0} - T_{2} + T_{4} - T_{6} + . . .)}_{0}^{2} + {(T_{1} - T_{3} + T_{5} + . . .)}_{1}^{2}

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represent the terms in the expansion of

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(T_{0} - T_{2} + T_{4} - \dots)^{2} + (T_{1} - T_{3} + T_{5} - \dots)^{2}

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