Question

11,22,33. In this arthematic sequence Find 30 th term. Find algebraic form. Find sum if first 25 terms.

Answer 1

First term(a) = 11

Common difference(d) = 22 - 11 = 11

Formula: nth term = a + (n - 1)d

(i): 30th term = 11 + (30 - 1)(11)

30th term = 330

(ii): Let any term be nth term = a + (n - 1)d = 11 + (n - 1)11

General term: 11 + 11n - 11

General term: 11n

Algebraic form is 11n

(iii): sum of n terms = (n/2) [2a + (n - 1)d]

Sum of 25 terms = (25/2) [2(11) + 24(11)]

Sum of 25 terms = 3575

Answer 2

$\red{ \qquad \underline{ \pmb{{ \mathbb{ \maltese  \:  COMPLETE \: \: QUESTION \:   \maltese }}}}}$

• 11,22,33. In this arthematic sequence Find 30 th term. Find algebraic form. Find sum if first 25 terms.

$\Large\green{\qquad\underline{\pmb{{ \mathbb { \maltese  \:  GIVEN \:  \maltese }}}}}$

Here ,

$a =t1 = 11$

$t2 = 22$

$t3 = 33$

$\purple{\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese  \:  REQUIRED \: \: INFO \:  \maltese }}}}}$

$d = t2 - t1= 22 - 11 = 11$

$\Large \orange{\qquad \underline{ \pmb{{ \mathbb{ \maltese  \: Formula \:  \maltese }}}}}$

$n \: term \: = a + (n - 1) \times d$

$\huge\boxed{\fcolorbox{pink}{ink}{TO FIND:}}$

$30 \: th \: term$

$\Large \orange{\qquad \underline{ \pmb{{ \mathbb{ \maltese  \: Solution \:  \maltese }}}}}$

${30 \: th \: term = 11 +( 13 - 1) \times 11}$

Therefore,

$30 \: th \: term = 330$

$\large \mathfrak{ \text{W}e \: \text{K}now }$

${General \: term = 11+(11n-11)}$

$General \: term = 11n$

Now :

Now :Sum of 25 term :

$Sn = \frac{n}{2} \times (2a + (n - 1) \times d)$

$\frac{25}{2} \times 2 \times 11 + (25- 1) \times 11$

$\huge\fbox\pink{✯Final Answer✯}$

• The Sum of 25 term is

$\huge\boxed{\dag\sf\blue{= 3575}\dag}$

$\huge\boxed{\dag\sf\red{Thanks}\dag}$