Question

4. If nth term of the A.P. 4, 7, 10, ________ is 82, then the value of n is​

Answer 1

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Answer 2

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

★ Given that,

How many terms are there in the AP : 4,7,10...82

★ Let,

• a1 = 4
• a2 = 7

Common difference (d) = a2 - a1

➡ 7 - 4

➡ 3

★ Now we have,

• a = 4
• d = 3
• an = 82
• n = ?

★ By using nth term formula :

$\tt\ a_{n}\:=a + (n \: - \: 1)d$

• Substitute the values.

$\tt\ \: ⟹ \: 82 \: = 4 + (n - 1) 3$

$\tt\ \: ⟹82 = 4 + 3n - 3$

$\tt\:⟹82 = 1+ 3n$

$\tt\:⟹82 - 1 = 3n$

$\tt\:⟹ 3n = 81$

$\tt\:⟹ n = \frac{81}{3}$

$\tt\:⟹ n = 27$

$\underline{\boxed{\bf{\purple{∴ The\:value\:of\:n\:is\:27}}}}$

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