Question

The first term of an AP.is 5, the common difference is 3 and the last term is 80; find a
number of terms.​

Answer 1

Answer:

26

Step-by-step explanation:

a =5,d=3 and an = 80

n =a +(n-1)d

according to the question,

80 = 5 + (n-1)3

75=(n-1)3

25=n-1

25 +1 =n

26=n

i.e.,in this AP,there are 26 no: of terms

Answer 2

Answer:

$\green{n=26}$

Step-by-step explanation:

$\large{Arithmatic..progression}$

first term=5=a

common diffrence=3=d

last term=80=An

then the number of terms will be

$\large{</strong><strong>An</strong><strong>=</strong><strong>a</strong><strong>+</strong><strong>(</strong><strong>n-1</strong><strong>)</strong><strong>d</strong><strong>}$

$\large{</strong><strong>8</strong><strong>0</strong><strong>=</strong><strong>5</strong><strong>+</strong><strong>(</strong><strong>n-1</strong><strong>)</strong><strong>3</strong><strong>}$

$\large{</strong><strong>8</strong><strong>0</strong><strong>-</strong><strong>5</strong><strong>=</strong><strong>(</strong><strong>n-1</strong><strong>)</strong><strong>3</strong><strong>}$

$\large{</strong><strong>7</strong><strong>5</strong><strong>=</strong><strong>(</strong><strong>n-1</strong><strong>)</strong><strong>3</strong><strong>}$

$\large{</strong><strong>7</strong><strong>5</strong><strong>/</strong><strong>3</strong><strong>=</strong><strong>n-1</strong><strong>}$

$\large{</strong><strong>2</strong><strong>5</strong><strong>=</strong><strong>n-1</strong><strong>}$

$\large{</strong><strong>2</strong><strong>5</strong><strong>+</strong><strong>1</strong><strong>=</strong><strong>n</strong><strong>}$

$\large{</strong><strong>2</strong><strong>6</strong><strong>=</strong><strong>n</strong><strong>}$