The values of several terms in a sequence are shown in the table. ![](http://admin.getprephub.com/media/editor/ag7_20230225140147671564.png) Find the first term, $$f(1)$$.

Given that, $$f(2)=5, f(4)=12, f(7)=22.5$$ Let, $$f(n)=f(1)+(n-1) d$$ Putting, $$n=2, f(2)=5=f(1)+d \ldots (i)$$ Putting, $$n=4, f(4)=12=f(1)+3 d \ldots (ii)$$ Putting, $$n=7, f(7)=22.5=f(1)+6 d \ldots (iii)$$ By $$(ii)-(i)$$, $$7=2 d$$ Or, $$d=3.5$$ Putting $$d=3.5$$ in $$(i)$$, $$5=f(1)+3.5$$ Or, $$5-3.5=f(1)$$ Or, $$f(1)=1.5$$

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MCQ

The values of several terms in a sequence are shown in the table.

Find the first term, $f(1)$ .

Select all that apply :

$1.5$

$3.5$

$2.5$

$4$

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