Question

Which term of the AP:3, 8, 13, 18,..... is78

Answer 1

Answer:

$ap = 3.8.13.18...........78$

$a = 3$

$d = 8 - 3 = 5 \: \\ d = 5$

$an = 78$

$an = a + {n - 1} \times d$

$78 = 3 + n - 1 \times 5$

$78 - 3 = n - 1 \times 5 \\ 75 = n - 1 \times 5$

$n - 1 \times 5 = 75$

$n - 1 = 75 \div 5 \\ n - 1 = 15$

$n = 15 + 1 = 16 \\ n = 16$

$so \: the \: 16th \: term \: of \: the \: ap \: is \: 78.$

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Answer 2

n=16

Step-by-step explanation:

In a mathematics Arithmetic progression/series in the sequence of a number difference between the consecutive term is constant where common difference is denoted by d and first term is denoted by a.Sum of $n^{th}$ term is denoted by Sn.

• First term is denoted by $a_1$.
• Second term is denoted by $a_2$.
• Common difference is equal to $a_2-a_1$.

According to question

Given that, a = 3

                an = 78

                  d = $a_2-a_1$ = 8-3 = 5

Now applying formula $an = a+(n-1)d$

                                     $78=3+(n-1)d$

                                     $78=3+5n-5\\78=-2+5n\\78+2=5n\\80=5n\\n=16$