एक A.P. में,
a₃ = 15 और S₁₀ = 125 दिया है। d और a₁₀ ज्ञात कीजिए।

यहाँ, a₃= 15
S₁₀ = 125
$straight S subscript straight n space equals space straight n over 2 space left square bracket space 2 straight a space plus space left parenthesis straight n space minus space 1 right parenthesis space straight d space right square bracket therefore space straight S subscript 10 space equals space 10 over 2 space left square bracket space 2 straight a space plus space left parenthesis 10 space minus space 1 right parenthesis space straight d space right square bracket rightwards double arrow space 125 space equals space 5 space straight x space left square bracket space 2 straight a space plus space 9 straight d space right square bracket rightwards double arrow space 2 straight a space plus space 9 straight d space equals space 125 over 5 space equals space 25 rightwards double arrow space 2 straight a space plus space 9 straight d space equals space 25 space space space space space space... left parenthesis straight i right parenthesis straight a subscript 3 space equals space straight a space plus space 2 straight d space equals space 15 rightwards double arrow space straight a space plus space 2 straight d space equals space 15 space space space space space space space space... left parenthesis ii right parenthesis$
समीकरण (i) और (ii) को हल करने पर
5d = - 5
$straight d space equals space minus space 5 over 5 space equals space minus space 1$
d का मान समीकरण (ii) में रखने पर
$straight a space plus space 2 space straight x space left parenthesis space minus 1 space right parenthesis space equals space 15 straight a space minus space 2 space equals space 15 straight a space equals space 17 straight a subscript 10 space equals space straight a space plus space 9 straight d straight a subscript 10 space equals space 17 space plus space 9 space straight x space left parenthesis space minus 1 right parenthesis straight a subscript 10 space equals space 17 space minus space 9 straight a subscript 10 space equals space 8 अत colon space straight d space equals space minus space 1 comma space space straight a subscript 10 space equals space 8$

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एक A.P. में,a3 = 15 और S10 = 125 दिया है। d और a10 ज्ञात कीजिए।

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गणित

एक A.P. में,
a₃ = 15 और S₁₀ = 125 दिया है। d और a₁₀ ज्ञात कीजिए।