Question

If the sum of first ‘n’ terms in an AP is 4n2 + 3n, then what is the 7th term of this AP

Answer 1

Answer:

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Answer 2

◘ Given ◘

Sum of first n terms of an AP is 4n² + 3n.

$\sf{\longrightarrow S_n=4n^2+3n}$

$\underline{\rule{180}4}$

◘ Objective ◘

To find the 7th term of this AP.

$\underline{\rule{180}4}$

◘ Solution ◘

We know,

$\sf{S_1=a_1}$

Putting the values :-

$\sf{a_1=S_1=4(1)^2+3(1)}\\\\\sf{\longmapsto a_1=4+3}\\\\\sf{\longmapsto a_1=7}$

___________

Similarly,

$\sf{S_2=a_1+a_2}\\\\\sf{\longmapsto S_2=7+a_2}\\\\\sf{\longmapsto 4(2)^2+3(2)=7+a_2}\\\\\sf{\longmapsto 8+11=7+a_2}\\\\\sf{\longmapsto 19=7+a_2}\\\\\sf{\longmapsto a_2=19-7}\\\\\sf{\longmapsto a_2=12}$

Common difference (d) = a₂ - a₁

$\sf{\longmapsto d = 12 - 7}$

$\sf{\longmapsto d = 5}$

The 7th term of the AP is :-

$\sf{a_7=a+(7-1)d}\\\\\sf{\longmapsto a_7=7+6(5)}\\\\\sf{\longmapsto a_7=7+30}\\\\\boxed{\sf{\color{navy}{\longmapsto a_7=37}}}$

Therefore, the 7th term of this AP is 37.