Question

5) Find the 20 term of the A.P 12,7, 2----​

Answer 1

Step-by-step explanation:

To find:-

$\sf t_{20}$

Solution:-

a=12

d=12-7=-5

$\qquad\sf\longmapsto t_20=a +(20-1)d$

$\qquad\sf\longmapsto 12+19×(-5)$

$\qquad\sf\longmapsto 12+(-95)$

$\qquad\sf\longmapsto12-95$

$\qquad\sf\longmapsto -83$

Answer 2

Answer:

$\large \underline {\sf \pmb {\red{Given}}}$

• ➠ A.P - 12 ,7, 2..

$\large {\underline {\sf \pmb{ \red{To Find}}}}$

• ➠ 20th term

$\large \underline{\sf\pmb {\red{Using \: Formula }}}$

$\circ{\underline {\boxed{ \sf{T_n=a+(n-1)d}}}}$

Where

• ➠ tn = nth term
• ➠ n = Number of Term
• ➠ a = First term
• ➠ d = Common deference

$\large \underline{\sf \pmb {\red{Solution}}}$

$\pink\bigstar \: \underline \frak{\pmb{Here \: we \: know \: that:}}$

• ⇒ First Term = 12
• ⇒ Number of Term = 20

$\pink\bigstar \: \underline\frak{\pmb{\: Finding \: Common \: Differences \: between \: terms}}$

$: \implies\sf{a_2-a_1}$

$: \implies \sf{7 - 12}$

$: \implies \sf{-5}$

• ➛ Hence, The common difference between terms is 6.

$\pink \bigstar \: \underline\frak{\pmb{Now \: Finding \: 20th \: Term}}$

$: \implies { \sf{T_n=a+(n-1)d}}$

• ⇒ Substituting the values

$\implies { \sf{T_{20}=12+(20-1) - 5}}$

$: \implies { \sf{T_{20}=7+(19 \times - 5)}}$

$: \implies { \sf{T_{20}=12 + ( - 95) }}$

$: \implies { \sf{T_{20}= - 8 3}}$

• ➛ Henceforth, The 20th term is -83.

$\large \underline{ \sf \pmb {\red{More \: Useful \: Formulae}}}$

★ Formula to find the numbers of term of an AP:

• $: \implies \sf{n= \bigg[ \dfrac{(l - a)}{d} \bigg]}$

★ Formula to find the tsum of first n terms of an AP:

• $: \implies\sf{S_n= \dfrac{n}{2} (a + l)}$

★ Formula to find the sum of squares of first n natural numbers of an AP:

• $: \implies \sf{S = \dfrac{n(n + 1)(2n + 1)}{6} }$

★ Formula to find the nth term of an AP is the square of the number of terms:

• $: \implies \sf{S = {n}^{2} }$

★ Formula to find the sum of of an AP:

• $: \implies \sf{S = n(n+1)}$