Maths / Arithmetic Progression / Find The Value of Nth Term when Common Difference, Number of Terms and First Term are Given

QUESTION

How many terms are there in the sequence 3, 6,9,12,......... 111?

EXPLANATION
Explain TypeExplanation Content
Text

3, 6,9,12,........

$\dpi{120} \fn_jvn \large d_1=a_2-a_1=6-3=3$

$\dpi{120} \fn_jvn \large d_2=a_3-a_2=9-6=3$

$\dpi{120} \fn_jvn \large as\; d_1=d_2, So\; the\; sequence\; is\; in\; AP$

$\dpi{120} \fn_jvn \large a= 3 \; d=3$

$\dpi{120} \fn_jvn \large a_n= a+ (n-1)d$

$\dpi{120} \fn_jvn \large 111= 3+ (n-1)3$

$\dpi{120} \fn_jvn \large 111= 3+ 3n-3 = 3n$

$\dpi{120} \fn_jvn \large n=\frac{111}{3}= 37$

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