Question

7th term of a sequence is 34 and 15th t term is 66 7 term of the sequence is 34 and 15th term is 66 , what is the common difference
, what is the 20th term write the 3 term , what is the algebric form of the sequence

Answer 1

$\huge† \huge \bold{\: \pmb {\red{ Answer }} }$

${\color{darkblue}{\textsf{\textbf{ Giνєη }}}}$

Consider the arithmetic sequence whose 7th term is 34. and 15th term is 66

• a) Find the common difference.
• b) Find the 20th term and next 3 terms

${\color{darkblue}{\textsf{\textbf{ ѕσlυтiση }}}}$

we know that, an arithmetic sequence with first term as a and common difference as d, than

• nth term of AP is = a + (n - 1)d.

given that, 7th term of AP is 34 and 15th term is 66.

So,

$\sf \: T_7 = a + (7 - 1)d \\ \\ \sf \implies 34a + 6d = 34 \: \:\: \: - - - - - Eqn.(1)$

and,

$\sf \: T_{15} = a + (15-1)d \\ \\ \sf \implies \: a +14d = 66 \: \: \: \: \: \: \: \: \: -------- Eqn.(2)$

subtracting Eqn.(1) from Eqn.(2) we get,

$\sf(a + 14d) - (a + 6d) = 66 - 34 \\ \\ \sf \longrightarrow a- a +14d - 6d = 32 \\ \\ \sf \longrightarrow 8d = 32 \\ \\\sf \longrightarrow d = \cancel \frac{32}{8} \\ \\ \sf \longrightarrow \: d = \red4$

Putting value of d in Eqn.(1),

$\sf \: a + 6d = 34 \\ \\ \sf \longrightarrow \: a + 6×4 = 34 \\ \\\sf \longrightarrow a + 24 = 34 \\ \\\sf \longrightarrow a=34-24 \\ \\\sf \longrightarrow a= \red{10}$

Therefore,

$\sf \: T_{20}= a + (20-1)d \\ \\ \sf \dashrightarrow T_{20} = 10+ 19 \times 4 \\ \\\sf \dashrightarrow T_{20} = 10 + 76 \\ \\\sf \dashrightarrow T_{20} = \red{ 86 }$

╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾

$\sf \: T_{21}= a + (21-1)d \\ \\ \sf \dashrightarrow T_{21} = 10+ 20 \times 4 \\ \\\sf \dashrightarrow T_{21} = 10 + 80 \\ \\\sf \dashrightarrow T_{21} = \red{ 90 }$

╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾

$\sf \: T_{22}= a + (22-1)d \\ \\ \sf \dashrightarrow T_{22} = 10+ 21 \times 4 \\ \\\sf \dashrightarrow T_{22} = 10 + 84 \\ \\\sf \dashrightarrow T_{22} = \red{ 94 }$

╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾╾

$\sf \: T_{23}= a + (23-1)d \\ \\ \sf \dashrightarrow T_{23} = 10+ 22 \times 4 \\ \\\sf \dashrightarrow T_{23} = 10 + 88 \\ \\\sf \dashrightarrow T_{23} = \red{ 98 }$

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