Question

which term of AP 3,8,13,18,...is78​

Answer 1

Answer:

• 16th term of AP is 78.

Step-by-step explanation:

Given:

• a\a₁ = 3
• a₂ = 8
• d = a₂ - a₁ = 8 - 3 = 5
• aₙ = 78

To Find:

• Which term of AP 3, 8, 13, 18,... is 78?

Now, by using this formula we will find which term is 78 of the given AP.

⇒ aₙ = a + (n - 1)d

⇒ 78 = 3 + (n - 1)5

⇒ 78 - 3 = (n - 1)5

⇒ 75/5 = (n - 1)

⇒ 15 = n - 1

⇒ 15 + 1 = n

⇒ n = 16

Hence, 16th term of AP is 78.

Important formulas of AP:

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

$\tt{\implies d=a_{2}-a_{1}}$

$\tt{\implies S_{n}=\dfrac{n}{2}[2a+(n-1)d]}$

$\tt{\implies S_{n}=\dfrac{n}{2}[a+l]}$

Where,

• a\a₁ = First term
• d = common difference
• a₂ = second term
• n = number of terms
• Sₙ = sum of nth terms
• l = last term

#answerwithquality

#BAL

Answer 2

Answer:

Given -

• a = 3
• d = 8 - 3 = 5
• $\sf{a}_{n}$ = 78
• n = ?

We know that,

$\\ \tt \implies \: a_n = a + (n - 1) \: d \\ \\ \\ \tt \implies \: 78 = 3 + (n - 1) (5) \\ \\ \\ \tt \implies \: 78 = 3 + 5n + 5 \\ \\ \\ \tt \implies \: 78 = - 2 + 5n \\ \\ \\ \tt \implies \: 80 = 5n \\ \\ \\ \implies \tt \: n = \frac{80}{5} \\ \\ \\ \implies \tt \blue{n = 16}$

78 will be the 16th term of the AP.