Question

which term of the AP 3,8,13,18........................... is 96?​

Answer 1

Answer:

a=3 , d=8-3=5 , an=96

an= a+ (n-1)d

96 = 3+ (n-1)5

96-3 = 5n-5

93+5 = 5n

98 = 5n

n = 98/5

n= 19.5

since n cannot be in decimal form therefore 96 is not the term of this Ap

Answer 2

$\huge\underline\mathbb{\red S\pink{O}\purple{L} \blue{UT} \orange{I}\green{ON :}}$

★ Given that,

which term of the AP 3,8,13,18........................... is 96?

★ Let,

• a1 = 3
• a2 = 8

Common difference (d) = a2 - a1

➡ 8 - 3 = 5

★ Now we have,

• a = 3
• d = 5
• an = 96

$\tt{By\;using\;n^{th}\:term\:formula }$

$\tt{⟹\:a_{n}\:=\:a\:+\:(n\:-\:1)d}$

• Substitute the values.

$\tt{⟹\:96\:=\:3\:+\:(n\:-\:1) 5}$

$\tt{⟹\:96\:=\:3\:+\:5n\:-\:5}$

$\tt{⟹\:96\:=\:5n\:-\:2}$

$\tt{⟹\:96\:+\:2=\:5n}$

$\tt{⟹\:98\:=\:5n}$

$\tt{⟹\:n\:=\:\frac{98}{5}}$

$\tt{⟹\:n\:=\:19.6}$

$\underline{\boxed{\bf{\purple{∴\:Hence\:the\:value\:n\:is\:in\:decimials.\:So,\:96\:is\:not\:a\:term\:of\:AP.}}}}$