Question

Determine the number of terms in the A.P. 3, 7, 11, ..., 399. Also, find its 20th term from the end.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Number\:of\:terms=100\:terms}}}$

$\green{\tt{\therefore{20th\:term\:from\:the\:end=323}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies A.P= 3,7,11,.....,399 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt:\implies Number\:of\:term\:in\:this\:A.P=?\\\\ \tt: \implies 20th \: term\:from\:the\:end= ?$

• According to given question :

$\tt \circ \: First \: term = 3 \\ \\ \tt \circ \: Common \: difference = 4 \\ \\ \tt \circ \: Last \: term = 399 \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies a_{n} = a + (n - 1) \times d \\ \\ \tt: \implies 399 = 3 + (n - 1) \times 4 \\ \\ \tt: \implies 399 - 3 = (n - 1) \times 4 \\ \\ \tt: \implies \frac{396}{4} = n - 1 \\ \\ \tt: \implies n - 1 = 99 \\ \\ \green{\tt: \implies n = 100 \: terms}$

$\circ \: \tt{First\:term\:from\:end=399} \\\\ \tt\circ\:Common\:difference=-4\\\\ \tt\circ\:Last\:term=3\\\\ \tt\circ\:n=20$

$\bold{As \: we \: know \: that} \\ \tt: \implies a_{n} = a +( n - 1)d \\ \\ \tt: \implies a_{20}= 399+ (20- 1) \times ( -4) \\ \\ \tt: \implies a_{20} = 399 +19 \times ( - 4) \\ \\ \tt: \implies a_{20} =399 - \\ \\ \green{\tt: \implies a_{20} =323} \\ \\ \green{\tt \therefore 323\: is \: the \: 20th \: term \: from \: the \: end}$

Answer 2

Answer:

$hey$

Step-by-step explanation:

3,7,11,.................,407

407= 3+(n-1)(4)    nth term = a+(n-1)d

 = 3+4n-4

 = 4n-1

 408=4n

n=408/4

n=102

Number of terms = 102

It we start from last

Then first term =407

common difference =(-4)

20th term = 407 + (20-1) (-4)

 = 407+ 19 * (-4)

 = 407 - 76  

     = 331 ans.