Question

$\boxed{\text{In an AP , prove that }}$
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$\bigstar \sf{t_p + t_{p + 2q} \:=\: 2•t_{p + q}}$​

Answer 1

Answer:

$To \: show \: that: \: t _{p} + t _{p} + _{2q} = 2t _{p} + _{q}$

Proof:

$t _{p} = a + (p - 1)d \: where \: a \: = first \: term \\ and \: d = common \: diffrence$

$t _{p + 2q} = a + (p + 2q - 1)d$

$∴t _{p} + t _{p + 2q} = a + (q - 1)d + a + (p + 2q - 1)d$

= a+ pd – d+ a+ pd +2qd-d

= 2a + 2pd + 2qd – 2d

= 2(a+ pd + qd - d)

= 2 [a + (p+q) d - d]

= 2 [a + (p+q-1)d]

$= 2T _{p + q}$

Hence proved.

Answer 2

Answer:

amar lagbe na

pey gachi already

do you know bengali if yes give a thanks